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new file mode 100644
index 0000000000000000000000000000000000000000..eafd81cb3ba9c80a40b37b5dab36669d5cc4c7fa
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+\relax 
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+\citation{mandl2010quantum}
+\citation{peskin2018introduction}
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+\newlabel{t.mu.nu.general}{{A.9}{9}}
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+\bibcite{peskin2018introduction}{2}
+\bibcite{asale_2021}{3}
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diff --git a/ejemplo_clase/MT_19.bbl b/ejemplo_clase/MT_19.bbl
new file mode 100644
index 0000000000000000000000000000000000000000..3f5b61c82b847715684662c3376e916bf0b1c572
--- /dev/null
+++ b/ejemplo_clase/MT_19.bbl
@@ -0,0 +1,17 @@
+\begin{thebibliography}{1}
+
+\bibitem{mandl2010quantum}
+Franz Mandl and Graham Shaw.
+\newblock {\em Quantum field theory}.
+\newblock John Wiley \& Sons, 2010.
+
+\bibitem{peskin2018introduction}
+Michael Peskin.
+\newblock {\em An introduction to quantum field theory}.
+\newblock CRC press, 2018.
+
+\bibitem{asale_2021}
+RAE ASALE.
+\newblock jurungar | diccionario de la lengua española, 2021.
+
+\end{thebibliography}
diff --git a/ejemplo_clase/MT_19.blg b/ejemplo_clase/MT_19.blg
new file mode 100644
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diff --git a/ejemplo_clase/MT_19.pdf b/ejemplo_clase/MT_19.pdf
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diff --git a/ejemplo_clase/MT_19.tex b/ejemplo_clase/MT_19.tex
new file mode 100644
index 0000000000000000000000000000000000000000..c92b08f9b786328ee3b8dd24259605887a7e2ddc
--- /dev/null
+++ b/ejemplo_clase/MT_19.tex
@@ -0,0 +1,81 @@
+\documentclass[12pt]{report}
+%\setlength{\columnseprule}{0.4pt}
+%\setlength{\columnsep}{3em}
+\usepackage[papersize={10in,6.5in},left=1in,right=2in]{geometry}
+\usepackage[utf8]{inputenc}
+\usepackage[spanish]{babel}
+
+\usepackage{wrapfig}
+%\def\changemargin#1#2{\list{}{\rightmargin#2\leftmargin#1}\item[]}
+%\let\endchangemargin=\endlist 
+
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amssymb}
+
+\usepackage{lipsum}
+
+\usepackage{blindtext}
+
+\usepackage{leading}
+\leading{18pt}
+
+%Footer
+
+\usepackage{lastpage}
+\usepackage{fancyhdr}
+\setlength{\headheight}{15.2pt}
+\pagestyle{fancy}
+\renewcommand{\chaptermark}[1]{\markboth{#1}{}}
+\fancyhf{}
+\fancyhead[LE,LO]{\chaptername~\thechapter:~\leftmark}
+%\fancyhead[LO]{\leftmark}
+%\fancyhead[LE,RO]{\thepage}
+
+%\fancyhead[LE,LO]{\thesection}
+%\fancyhead[RE,RO]{\chaptername~\thechapter}
+\lfoot[\tiny Versión. Fecha: \today]{\tiny Versión. Fecha: \today}
+\cfoot[\thepage/\pageref{LastPage}]{\thepage/\pageref{LastPage}}
+%\rfoot[<even output>]{\thepage/\pageref{LastPage}}
+
+
+%Tipo de letra
+%\renewcommand{\familydefault}{\sfdefault}
+
+
+%Tikz pictures
+\usepackage{tikz}
+\usetikzlibrary{babel}
+\usetikzlibrary{decorations.markings}
+
+\usepackage{pgfplots}
+%\pgfplotsset{compat=1.15} 
+
+%Alinear texto y figuras en las tablas
+\usepackage{adjustbox}
+\title{Campo de Dirac}
+\author{José Antonio López Rodríguez}
+\makeindex
+
+\input{qftdef.tex}
+
+\begin{document}
+\maketitle
+\tableofcontents
+
+\input{seccion_campo_dirac.tex}
+
+\appendix
+\chapter{Glosario}
+\input{apendice_glosario.tex}
+
+\bibliographystyle{unsrt}
+\bibliography{particulas}
+
+\end{document}
+
+
+
+
+
+
diff --git a/ejemplo_clase/MT_19.toc b/ejemplo_clase/MT_19.toc
new file mode 100644
index 0000000000000000000000000000000000000000..5573fec79f576ad0e06332ca51358722ba513f16
--- /dev/null
+++ b/ejemplo_clase/MT_19.toc
@@ -0,0 +1,6 @@
+\select@language {spanish}
+\contentsline {chapter}{\numberline {1}Campo de Dirac}{2}
+\contentsline {section}{\numberline {1.1}Sobre la representaci\IeC {\'o}n de n\IeC {\'u}mero en fermiones}{3}
+\contentsline {section}{\numberline {1.2}Sobre la representaci\IeC {\'o}n de n\IeC {\'u}mero para fermiones}{6}
+\contentsline {section}{\numberline {1.3}El Campo de Dirac}{7}
+\contentsline {chapter}{\numberline {A}Glosario}{8}
diff --git a/ejemplo_clase/apendice_glosario.tex b/ejemplo_clase/apendice_glosario.tex
new file mode 100644
index 0000000000000000000000000000000000000000..d655afcd5a672ac1041c75b59b7d1be1f1a31f92
--- /dev/null
+++ b/ejemplo_clase/apendice_glosario.tex
@@ -0,0 +1,27 @@
+\begin{itemize}
+\item Definimos la métrica de Minkowski usando la convención 
+\begin{equation}
+\label{convencion.metrica}
+\eta_{\mu\nu}=diag(+,-,-,-)
+\end{equation}
+\item Definimos los operadores de Laplace y de D'Alambert:
+\begin{eqnarray}
+\nabla^2 & \equiv & \sum_i\partial_i^2 \\
+\square & \equiv & \partial_{0}^{2} - \nabla^2 = \partial_{\mu}\partial^{\mu} 
+\end{eqnarray}
+\item Forma general de las corrientes de Noether para un sistema con campos $\phi_i$, lagrangiano $\mathcal{L}$ y grupo de simetría de la acción con parámetros $\epsilon^{I}$:
+\begin{eqnarray}\label{J.noether.general}
+{J^{\mu}}&=&\Pi^{i\mu}\delta\phi_i-{T^{\mu}}_{\nu}\delta x^{\nu}, \\
+{J^{\mu}}_{I}&=&\Pi^{i\mu}\frac{\partial\phi_i}{\partial\epsilon^{I}}-{T^{\mu}}_{\nu}\frac{\partial x^{\nu}}{\partial\epsilon^{I}}.
+\end{eqnarray}
+
+Donde
+\begin{eqnarray}
+\delta x^{\nu} &=& \frac{\partial x^{\nu}}{\partial\epsilon^{I}}\delta\epsilon^{I}, \\
+\delta\phi_i &=& \frac{\partial\phi_i}{\partial\epsilon^{I}}\delta\epsilon^{I}, \\
+\Pi^{i\mu} &=& \frac{\partial\mathcal{L}}{\partial\partial_{\mu}\phi_{i}}, \label{momento.lagrangiano.general}\\
+{T^{\mu}}_{\nu} &=& \Pi^{i\mu}\partial_{\nu}\phi_{i} - \delta^{\mu}_{\nu} \mathcal{L}.\label{t.mu.nu.general}
+\end{eqnarray}
+
+
+\end{itemize}
\ No newline at end of file
diff --git a/ejemplo_clase/particulas.bib b/ejemplo_clase/particulas.bib
new file mode 100644
index 0000000000000000000000000000000000000000..6c9a72efa6c81c66fd5de7ce9142661396ebe988
--- /dev/null
+++ b/ejemplo_clase/particulas.bib
@@ -0,0 +1,22 @@
+@book{mandl2010quantum,
+  title={Quantum field theory},
+  author={Mandl, Franz and Shaw, Graham},
+  year={2010},
+  publisher={John Wiley \& Sons}
+}
+
+@book{peskin2018introduction,
+  title={An introduction to quantum field theory},
+  author={Peskin, Michael},
+  year={2018},
+  publisher={CRC press}
+}
+
+
+@misc{asale_2021,
+	title={jurungar | Diccionario de la lengua española},
+	url={https://dle.rae.es/jurungar},
+	journal={«Diccionario de la lengua española» - Edición del Tricentenario},
+	author={ASALE, RAE},
+	year={2021}
+	}
diff --git a/ejemplo_clase/propagador.tex b/ejemplo_clase/propagador.tex
new file mode 100644
index 0000000000000000000000000000000000000000..341eae9aa9619a2c4a9eb658779cdd65b7c3f2b6
--- /dev/null
+++ b/ejemplo_clase/propagador.tex
@@ -0,0 +1,65 @@
+\documentclass{article}
+\usepackage{tikz}
+\usetikzlibrary{decorations.markings}
+%https://tex.stackexchange.com/questions/361324/adding-arrows-to-a-complex-contour-with-tikz
+%https://tex.stackexchange.com/questions/166772/problem-with-babel-and-tikz-using-draw
+\begin{document}
+\begin{figure}
+
+\begin{tikzpicture}
+  [line width=.8pt,
+    decoration={%
+      markings,
+      %mark=at position 0.25 with {\arrow[line width=1pt]{>}},
+      mark=at position 0.5 with {\arrow[line width=1pt]{>}},    
+      %mark=at position 0.75 with {\arrow[line width=1pt]{>}}    
+    }
+  ]
+  \draw [help lines,->] (-4,0) -- (4,0) coordinate (xaxis);
+  \draw [help lines,->] (0,-1)coordinate(-yaxis) -- (0,4) coordinate (yaxis);
+  \node  at (1.5,-0.5) {$\bullet$};
+  \node  at (-1.5,-0.5) {$\bullet$};
+  \draw [postaction=decorate] (3,0) arc (0:180:3) ;
+  %\draw [postaction=decorate] (-3,0) --(-2,0) arc  (180:0:.5) --(1,0) arc  (180:0:.5)--(3,0) ;
+  \draw [postaction=decorate] (-3,0) --(3,0) ;
+  \node [below] at (xaxis) {$k_0$};
+  \node [above] at (yaxis) {$ik_0'$};
+  %\node [below left] {$O$};
+  %\node at (-1.5,.8) {$\gamma_{1}$};
+  %\node at (1.5,.8) {$\gamma_{2}$};
+  %\node at (2,3) {$\Gamma_{1}$};
+  \node at (3,-.5){$R$};
+  \node at (-3,-.5){$-R$};
+  \node at (1.5,-0.75){$(\omega_k-i\epsilon)$};
+  \node at (-1.5,-0.75){$-(\omega_k+i\epsilon)$};
+\end{tikzpicture}
+
+\end{figure}
+
+\begin{tikzpicture}
+  [yscale=-1,line width=.8pt,
+    decoration={%
+      markings,
+      mark=at position 0.25 with {\arrow[line width=1pt]{>}},
+      mark=at position 0.5 with {\arrow[line width=1pt]{>}},    
+      mark=at position 0.75 with {\arrow[line width=1pt]{>}}    
+    }
+  ]
+  \draw [help lines,->] (-4,0) -- (4,0) coordinate (xaxis);
+  \draw [help lines,->] (0,-1)coordinate(-yaxis) -- (0,4) coordinate (yaxis);
+  \node  at (1.5,0) {$\times$};
+  \node  at (-1.5,0) {$\times$};
+  \draw [postaction=decorate] (3,0) arc (0:180:3) ;
+  \draw [postaction=decorate] (-3,0) --(-2,0) arc  (180:0:.5) --(1,0) arc  (180:0:.5)--(3,0) ;
+  \node [below] at (xaxis) {$Re(z)$};
+  \node [above] at (-yaxis) {$Im(z)$};
+  \node [below left] {$O$};
+  \node at (-1.5,.8) {$\gamma_{1}$};
+  \node at (1.5,.8) {$\gamma_{2}$};
+  \node at (2,3) {$\Gamma_{2}$};
+  \node at (3,-.5){$R$};
+  \node at (-3,-.5){$-R$};
+  \node at (1.5,-.5){$1$};
+  \node at (-1.5,-.5){$-1$};
+\end{tikzpicture}
+\end{document}
\ No newline at end of file
diff --git a/ejemplo_clase/propagador_retardado.tex b/ejemplo_clase/propagador_retardado.tex
new file mode 100644
index 0000000000000000000000000000000000000000..9cd7fdea89336fa008bf80c609032dd7a662885f
--- /dev/null
+++ b/ejemplo_clase/propagador_retardado.tex
@@ -0,0 +1,61 @@
+%\begin{center}
+\begin{figure}
+\begin{tikzpicture}
+  [scale=0.8,line width=.8pt,
+    decoration={%
+      markings,
+      mark=at position 0.25 with {\arrow[line width=1pt]{>}},
+      %mark=at position 0.5 with {\arrow[line width=1pt]{>}},    
+      mark=at position 0.75 with {\arrow[line width=1pt]{>}}    
+    }
+  ]
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+  \draw [help lines,->] (0,-1)coordinate(-yaxis) -- (0,4) coordinate (yaxis);
+  \node  at (1.5,-0.5) {$\bullet$};
+  \node  at (-1.5,-0.5) {$\bullet$};
+  \draw [postaction=decorate] (3,0) arc (0:180:3) ;
+  %\draw [postaction=decorate] (-3,0) --(-2,0) arc  (180:0:.5) --(1,0) arc  (180:0:.5)--(3,0) ;
+  \draw [postaction=decorate] (-3,0) --(3,0) ;
+  \node [below] at (xaxis) {$k_0$};
+  \node [above] at (yaxis) {$ik_0'$};
+  %\node [below left] {$O$};
+  %\node at (-1.5,.8) {$\gamma_{1}$};
+  %\node at (1.5,.8) {$\gamma_{2}$};
+  %\node at (2,3) {$\Gamma_{1}$};
+  %\node at (3,-.5){$R$};
+  %\node at (-3,-.5){$-R$};
+  \node at (1.5,-0.95){$\scriptstyle (\omega_k-i\epsilon)$};
+  \node at (-1.5,-0.95){$\scriptstyle -(\omega_k+i\epsilon)$};
+  \node at (2,3.2){$x_0<0$};
+\end{tikzpicture}
+\begin{tikzpicture}
+  [scale=0.8,yscale=-1,line width=.8pt,
+    decoration={%
+      markings,
+      mark=at position 0.25 with {\arrow[line width=1pt]{>}},
+      %mark=at position 0.5 with {\arrow[line width=1pt]{>}},    
+      mark=at position 0.75 with {\arrow[line width=1pt]{>}}    
+    }
+  ]
+  \draw [help lines,->] (-4,0) -- (4,0) coordinate (xaxis);
+  \draw [help lines,->] (0,-1)coordinate(-yaxis) -- (0,4) coordinate (yaxis);
+  \node  at (1.5,-0.5) {$\bullet$};
+  \node  at (-1.5,-0.5) {$\bullet$};
+  \draw [postaction=decorate] (3,0) arc (0:180:3) ;
+  %\draw [postaction=decorate] (-3,0) --(-2,0) arc  (180:0:.5) --(1,0) arc  (180:0:.5)--(3,0) ;
+  \draw [postaction=decorate] (-3,0) --(3,0) ;
+  \node [below] at (xaxis) {$k_0$};
+  \node [above] at (-yaxis) {$ik_0'$};
+  \node [below left] {$O$};
+  %\node at (-1.5,.8) {$\gamma_{1}$};
+  %\node at (1.5,.8) {$\gamma_{2}$};
+  %\node at (2,3) {$\Gamma_{2}$};
+  \node at (2,3) {$x_0>0$};
+  %\node at (3,-.5){$R$};
+  %\node at (-3,-.5){$-R$};
+  \node at (1.5,-.95){$\scriptstyle (\omega_k+i\epsilon)$};
+  \node at (-1.5,-.95){$\scriptstyle -(\omega_k-i\epsilon)$};
+\end{tikzpicture}
+\caption{Contornos de integración para el propagador retardado \label{contornos.propagador.retardado}}
+\end{figure}
+%\end{center}
diff --git a/ejemplo_clase/prueba.aux b/ejemplo_clase/prueba.aux
new file mode 100644
index 0000000000000000000000000000000000000000..48661e851a9354955f330cc8a98daa54af344764
--- /dev/null
+++ b/ejemplo_clase/prueba.aux
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+\citation{peskin2018introduction}
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diff --git a/ejemplo_clase/prueba.bbl b/ejemplo_clase/prueba.bbl
new file mode 100644
index 0000000000000000000000000000000000000000..531ffa2b4be1d61d4da17dc51a9bf346ea048509
--- /dev/null
+++ b/ejemplo_clase/prueba.bbl
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+\begin{thebibliography}{1}
+
+\bibitem{mandl2010quantum}
+Franz Mandl and Graham Shaw.
+\newblock {\em Quantum field theory}.
+\newblock John Wiley \& Sons, 2010.
+
+\bibitem{peskin2018introduction}
+Michael Peskin.
+\newblock {\em An introduction to quantum field theory}.
+\newblock CRC press, 2018.
+
+\end{thebibliography}
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new file mode 100644
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+\documentclass[11pt,twocolumn]{book}
+%\setlength{\columnseprule}{0.4pt}
+\setlength{\columnsep}{3em}
+\usepackage[papersize={10in,6.5in},margin=0.5in]{geometry}
+\usepackage[utf8]{inputenc}
+\usepackage[spanish]{babel}
+
+
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amssymb}
+
+\usepackage{lipsum}
+
+\usepackage{blindtext}
+
+\usepackage{leading}
+\leading{15pt}
+
+%Footer
+
+\usepackage{lastpage}
+\usepackage{fancyhdr}
+\setlength{\headheight}{15.2pt}
+\pagestyle{fancy}
+\renewcommand{\chaptermark}[1]{\markboth{#1}{}}
+\fancyhf{}
+\fancyhead[LE,LO]{\chaptername~\thechapter:~\leftmark}
+%\fancyhead[LO]{\leftmark}
+%\fancyhead[LE,RO]{\thepage}
+
+%\fancyhead[LE,LO]{\thesection}
+%\fancyhead[RE,RO]{\chaptername~\thechapter}
+\lfoot[\tiny Versión. Fecha: \today]{\tiny Versión. Fecha: \today}
+\cfoot[\thepage/\pageref{LastPage}]{\thepage/\pageref{LastPage}}
+%\rfoot[<even output>]{\thepage/\pageref{LastPage}}
+
+
+%Tipo de letra
+%\renewcommand{\familydefault}{\sfdefault}
+
+
+%Tikz pictures
+\usepackage{tikz}
+\usetikzlibrary{babel}
+\usetikzlibrary{decorations.markings}
+
+\usepackage{pgfplots}
+%\pgfplotsset{compat=1.15} 
+
+%Alinear texto y figuras en las tablas
+\usepackage{adjustbox}
+\title{Campo de Dirac}
+\author{José Antonio López Rodríguez}
+\makeindex
+
+\input{qftdef.tex}
+
+\begin{document}
+\maketitle
+\tableofcontents
+\chapter{Campo de Dirac}
+\input{seccion_campo_dirac.tex}
+\chapter{Prueba}
+\lipsum[5-20]
+
+\begin{center}
+\begin{figure}[h]
+\begin{tikzpicture}
+\begin{axis}[
+    x tick label style={
+        /pgf/number format/1000 sep=},
+    xlabel=Year,
+    enlargelimits=0.05,
+    legend style={at={(0.5,-0.2)},
+    anchor=north,legend columns=-1},
+    ybar interval=.7,
+]
+\addplot 
+    coordinates {(2020,7) (2019,6)
+         (2018,3.5) (2017,4) (2016,3)};
+\addplot 
+    coordinates {(2020,3) (2019,4) 
+        (2018,4) (2017,6) (2016,7)};
+\legend{A,B}
+\end{axis}
+\end{tikzpicture}
+\caption[jr]{Tomado de: https://tex.stackexchange.com/questions/501238/how-to-center-single-column-pgfplots-bar-graph-in-two-column-document}
+\end{figure}
+\end{center}
+
+\lipsum[1-2]
+
+\section{a}
+\lipsum[1-10]
+\appendix
+\chapter{Glosario}
+\input{apendice_glosario.tex}
+
+\bibliographystyle{unsrt}
+\bibliography{particulas}
+
+\end{document}
+
+
+
+
+
+
diff --git a/ejemplo_clase/prueba.toc b/ejemplo_clase/prueba.toc
new file mode 100644
index 0000000000000000000000000000000000000000..6f5fd785b02cdc67b71b62904bf6a53ee437dd5d
--- /dev/null
+++ b/ejemplo_clase/prueba.toc
@@ -0,0 +1,6 @@
+\select@language {spanish}
+\contentsline {chapter}{\numberline {1}Campo de Dirac}{5}
+\contentsline {section}{\numberline {1.1}Sobre la representaci\IeC {\'o}n de n\IeC {\'u}mero en fermiones}{5}
+\contentsline {chapter}{\numberline {2}Prueba}{7}
+\contentsline {section}{\numberline {2.1}a}{11}
+\contentsline {chapter}{\numberline {A}Glosario}{15}
diff --git a/ejemplo_clase/prueba_old.tex b/ejemplo_clase/prueba_old.tex
new file mode 100644
index 0000000000000000000000000000000000000000..937211ce9e26f7ab4d13bebf1a7a033cb25876ad
--- /dev/null
+++ b/ejemplo_clase/prueba_old.tex
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+\documentclass[12pt,letterpaper]{article}
+\usepackage[utf8]{inputenc}
+\usepackage[spanish]{babel}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amssymb}
+\author{José Antonio López Rodríguez}
+\begin{document}
+Hola mundo
+\end{document}
\ No newline at end of file
diff --git a/ejemplo_clase/qftdef.tex b/ejemplo_clase/qftdef.tex
new file mode 100644
index 0000000000000000000000000000000000000000..d975b80d514e5837aee9bf834181f382fd3675a3
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+\newcommand{\comm}[2]{
+	[#1,#2]
+}
+
+\newcommand{\commEn}[2]{
+	\left[#1,#2\right]
+}
+
+\newcommand{\ket}[1]{|#1>}
+
+\newcommand{\opA}[1]{a_{#1}^{{}}}
+
+\newcommand{\opAdaga}[1]{a_{#1}^{\dagger}}
\ No newline at end of file
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index 0000000000000000000000000000000000000000..4a6c2d8d51009cb4f68b0b645638742abfd08039
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+ %&-line parsing enabled.
+**seccion_campo_dirac.tex
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+Type  H <return>  for immediate help.
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+                                                  
+l.1 E
+     l Campo de Dirac es el objeto más importante en la descripción de par...
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+Missing character: There is no e in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no à in font nullfont!
+Missing character: There is no ³ in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no . in font nullfont!
+
+Overfull \hbox (20.0pt too wide) in paragraph at lines 5--6
+[]
+ []
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.7 T
+     enemos una serie de operadores de creación y destrucción de modos, et...
+
+You're in trouble here.  Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+Missing character: There is no T in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no e in font nullfont!
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+Missing character: There is no d in font nullfont!
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+Missing character: There is no s in font nullfont!
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+Missing character: There is no e in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no t in font nullfont!
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+Missing character: There is no g in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no à in font nullfont!
+Missing character: There is no © in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no e in font nullfont!
+
+Overfull \hbox (20.0pt too wide) in paragraph at lines 7--8
+[]
+ []
+
+
+Overfull \hbox (26.69896pt too wide) in paragraph at lines 7--8
+\OML/cmm/m/it/10 r; s []$ 
+ []
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.9 \begin{eqnarray*}
+                     
+You're in trouble here.  Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+
+Overfull \hbox (20.0pt too wide) in paragraph at lines 9--9
+[] 
+ []
+
+! Undefined control sequence.
+l.10 	\comm
+           {a_r}{a_s^{\dagger}} & = & \delta_{rs}, \\
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+! Undefined control sequence.
+<recently read> \comm 
+                      
+l.11 	\comm
+           {a_r}{a_s} & = & 0, \\
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+! Undefined control sequence.
+<recently read> \comm 
+                      
+l.12 	\comm
+           {a_r^{\dagger}}{a_s^{\dagger}} & = & 0.
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+
+Overfull \hbox (44.14359pt too wide) in alignment at lines 9--13
+ [][][] []
+ []
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.19 C
+      onsideramos el campo escalar en sus versiones real y complejo. Para co...
+
+You're in trouble here.  Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+Missing character: There is no C in font nullfont!
+Missing character: There is no o in font nullfont!
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+Missing character: There is no o in font nullfont!
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+Missing character: There is no a in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no c in font nullfont!
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+Missing character: There is no d in font nullfont!
+Missing character: There is no e in font nullfont!
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+Missing character: There is no c in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no p in font nullfont!
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+Missing character: There is no e in font nullfont!
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+Missing character: There is no a in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no a in font nullfont!
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+Missing character: There is no e in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no : in font nullfont!
+
+Overfull \hbox (20.0pt too wide) in paragraph at lines 19--20
+[]
+ []
+
+! Undefined control sequence.
+l.21 \mathcal{S}=\int {\rm
+                           d}^4 x \mathcal{L}=-\frac{1}{2}\int {\rm d}^4 x \...
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+! Undefined control sequence.
+l.21 ...m d}^4 x \mathcal{L}=-\frac{1}{2}\int {\rm
+                                                   d}^4 x \left(\partial_{\m...
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+
+Overfull \hbox (196.38503pt too wide) detected at line 22
+[]\OMS/cmsy/m/n/10 S \OT1/cmr/m/n/10 = [] \OML/cmm/m/it/10 d[]x\OMS/cmsy/m/n/10
+ L \OT1/cmr/m/n/10 = \OMS/cmsy/m/n/10 ^^@[] [] \OML/cmm/m/it/10 d[]x [] :
+ []
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.24 E
+      l funcional $\mathcal{S}$ se hace extremo si el campo $\phi$ cumple la...
+
+You're in trouble here.  Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+Missing character: There is no E in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no f in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no s in font nullfont!
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+Missing character: There is no h in font nullfont!
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+Missing character: There is no c in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no x in font nullfont!
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+
+Overfull \hbox (20.0pt too wide) in paragraph at lines 24--25
+[]
+ []
+
+
+Overfull \hbox (6.80551pt too wide) in paragraph at lines 24--25
+\OMS/cmsy/m/n/10 S$
+ []
+
+
+Overfull \hbox (5.95834pt too wide) in paragraph at lines 24--25
+\OML/cmm/m/it/10 ^^^$
+ []
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.26 \begin{equation}
+                     \label{ecuacion.KG}
+You're in trouble here.  Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+
+Overfull \hbox (20.0pt too wide) in paragraph at lines 26--26
+[] 
+ []
+
+
+! LaTeX Error: Command \Box not provided in base LaTeX2e.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.27 \left(\Box
+                + m^2\right)\phi=0.
+Load the latexsym or the amsfonts package to define this symbol
+
+
+Overfull \hbox (58.94678pt too wide) detected at line 28
+[][] \OML/cmm/m/it/10 ^^^ \OT1/cmr/m/n/10 = 0\OML/cmm/m/it/10 :
+ []
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.30 L
+      a ecuación (\ref{ecuacion.KG}) implica que el campo $\phi$ tiene solu...
+
+You're in trouble here.  Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+Missing character: There is no L in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no à in font nullfont!
+Missing character: There is no ³ in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no ( in font nullfont!
+! Undefined control sequence.
+<write> ...ference `ecuacion.KG' on page \thepage 
+                                                  \space undefined\on@line .
+l.30 La ecuación (\ref{ecuacion.KG}
+                                    ) implica que el campo $\phi$ tiene solu...
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+
+LaTeX Warning: Reference `ecuacion.KG' on page  undefined on input line 30.
+
+Missing character: There is no ) in font nullfont!
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+Missing character: There is no m in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no q in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no i in font nullfont!
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+Missing character: There is no o in font nullfont!
+Missing character: There is no o in font nullfont!
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+Missing character: There is no d in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no a in font nullfont!
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+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.32 S
+      e puede hallar la solución más general de la ecuación (\ref{ecuacio...
+
+You're in trouble here.  Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
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+! Undefined control sequence.
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+                                                  \space undefined\on@line .
+l.32 ...general de la ecuación (\ref{ecuacion.KG}
+                                                  ), pasando al espacio de F...
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
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+and I'll forget about whatever was undefined.
+
+
+LaTeX Warning: Reference `ecuacion.KG' on page  undefined on input line 32.
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+
+
+Overfull \hbox (10.86105pt too wide) in paragraph at lines 32--33
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+ []
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.34 \begin{equation}
+                     \label{solucion.KG.real.ondas.planas}
+You're in trouble here.  Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
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+and I'll forget about whatever was undefined.
+
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+
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+
+
+Overfull \hbox (158.40384pt too wide) in alignment at lines 38--41
+ [][][] []
+ []
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.43 L
+      a función $f_{\vec{k}}(x)$, con la definición de $\omega_k$ satisfac...
+
+You're in trouble here.  Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
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+! Undefined control sequence.
+<write> ...KG.real.ondas.planas' on page \thepage 
+                                                  \space undefined\on@line .
+l.43 ...sión (\ref{solucion.KG.real.ondas.planas}
+                                                  ). Además, la normalizaci...
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+
+LaTeX Warning: Reference `solucion.KG.real.ondas.planas' on page  undefined on 
+input line 43.
+
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+
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+
+Overfull \hbox (10.86105pt too wide) in paragraph at lines 43--44
+[]
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+
+Overfull \hbox (97.71538pt too wide) in alignment at lines 44--48
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+
+Overfull \hbox (30.98619pt too wide) in paragraph at lines 48--55
+      $\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 f[]; f[]\OT1/cmr/m/n/10 )$
+ []
+
+! Undefined control sequence.
+l.57 (f_1,f_2) &=& i\int {\rm
+                              d}^3x\bar{f}_1{\begin{array}{c}
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+! Undefined control sequence.
+l.63  &=& i\int {\rm
+                     d}^3 x (\bar{f}_1\partial_{0}f_2 - (\partial_{0}\bar{f}...
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+
+Overfull \hbox (158.62247pt too wide) in alignment at lines 55--64
+ [][][] []
+ []
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.66 P
+      ara construir soluciones particulares de la ecuación de Klein-Gordon ...
+
+You're in trouble here.  Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
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+! Undefined control sequence.
+<write> ...ference `ecuacion.KG' on page \thepage 
+                                                  \space undefined\on@line .
+l.66 ...ogénea de la ecuación (\ref{ecuacion.KG}
+                                                  )
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+
+LaTeX Warning: Reference `ecuacion.KG' on page  undefined on input line 66.
+
+Missing character: There is no ) in font nullfont!
+
+Overfull \hbox (20.0pt too wide) in paragraph at lines 66--67
+[]
+ []
+
+
+Overfull \hbox (10.86105pt too wide) in paragraph at lines 66--67
+[] 
+ []
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.68 \begin{equation}
+                     \label{ecuacion.KG.con.fuentes}
+You're in trouble here.  Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+
+Overfull \hbox (20.0pt too wide) in paragraph at lines 68--68
+[] 
+ []
+
+
+! LaTeX Error: Command \Box not provided in base LaTeX2e.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.69 \left(\Box
+                + m^2\right)\phi=\rho.
+Load the latexsym or the amsfonts package to define this symbol
+
+
+Overfull \hbox (59.11691pt too wide) detected at line 70
+[][] \OML/cmm/m/it/10 ^^^ \OT1/cmr/m/n/10 = \OML/cmm/m/it/10 ^^Z:
+ []
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.72 S
+      e define $G(x-x')$ tal que
+You're in trouble here.  Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+Missing character: There is no S in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no f in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no n in font nullfont!
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+Missing character: There is no l in font nullfont!
+Missing character: There is no q in font nullfont!
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+
+Overfull \hbox (20.0pt too wide) in paragraph at lines 72--73
+[]
+ []
+
+
+Overfull \hbox (25.24446pt too wide) in paragraph at lines 72--73
+\OML/cmm/m/it/10 G\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x \OMS/cmsy/m/n/10 ^^@
+ []
+
+
+Overfull \hbox (12.40973pt too wide) in paragraph at lines 72--73
+\OML/cmm/m/it/10 x[]\OT1/cmr/m/n/10 )$
+ []
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.74 \begin{eqnarray}
+                     \label{ecuacion.propagador.KG.real}
+You're in trouble here.  Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+
+Overfull \hbox (20.0pt too wide) in paragraph at lines 74--74
+[] 
+ []
+
+
+! LaTeX Error: Command \Box not provided in base LaTeX2e.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.75 && \left(\Box
+                  _x + m^2\right)G(x-x')=\delta^4(x-x'),\\
+Load the latexsym or the amsfonts package to define this symbol
+
+! Undefined control sequence.
+l.76 &\Rightarrow & \phi(x) = \phi_H(x) + \int{\rm
+                                                   d}^4 x' G(x-x')\rho(x'),
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+
+Overfull \hbox (178.2665pt too wide) in alignment at lines 74--77
+ [][][] []
+ []
+
+Missing character: There is no d in font nullfont!
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+Missing character: There is no d in font nullfont!
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+Missing character: There is no c in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no à in font nullfont!
+Missing character: There is no ³ in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no e in font nullfont!
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+Missing character: There is no a in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no c in font nullfont!
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+Missing character: There is no a in font nullfont!
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+Missing character: There is no à in font nullfont!
+Missing character: There is no ³ in font nullfont!
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+Missing character: There is no h in font nullfont!
+Missing character: There is no o in font nullfont!
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+Missing character: There is no e in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no ( in font nullfont!
+! Undefined control sequence.
+<write> ...ference `ecuacion.KG' on page \thepage 
+                                                  \space undefined\on@line .
+l.78 ...la ecuación homogénea (\ref{ecuacion.KG}
+                                                  ).
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+
+LaTeX Warning: Reference `ecuacion.KG' on page  undefined on input line 78.
+
+Missing character: There is no ) in font nullfont!
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+
+Overfull \hbox (27.03615pt too wide) in paragraph at lines 77--79
+ $\OML/cmm/m/it/10 ^^^[]\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x\OT1/cmr/m/n/10 )$
+ []
+
+
+Overfull \hbox (10.86105pt too wide) in paragraph at lines 77--79
+[] 
+ []
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.80 C
+      omo es acostumbrado se escribe la solución de la ecuación (\ref{ecua...
+
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+If that doesn't work, type  X <return>  to quit.
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+l.80 ...uación (\ref{ecuacion.propagador.KG.real}
+                                                  ) en el espacio de Fourier,
+The control sequence at the end of the top line
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+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.82 \begin{equation}
+                     
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+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.88 A
+       partir de (\ref{propagador.KG.fourier}) se definen los propagadores r...
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+You're in trouble here.  Try typing  <return>  to proceed.
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+! LaTeX Error: Missing \begin{document}.
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+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.90 \begin{eqnarray}
+                     
+You're in trouble here.  Try typing  <return>  to proceed.
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+
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+Overfull \hbox (20.0pt too wide) in paragraph at lines 90--90
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+
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+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.96 S
+      i en cambio la componente infinitesimal es positiva se define el propa...
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+
+Overfull \hbox (20.0pt too wide) in paragraph at lines 96--97
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+Overfull \hbox (87.87372pt too wide) detected at line 99
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+ []
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.101 X
+       XXXX
+You're in trouble here.  Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
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+
+Overfull \hbox (20.0pt too wide) in paragraph at lines 101--102
+[] 
+ []
+
+(./propagador_retardado.tex
+
+! LaTeX Error: Environment figure undefined.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.2 \begin{figure}
+                  
+Your command was ignored.
+Type  I <command> <return>  to replace it with another command,
+or  <return>  to continue without it.
+
+
+! LaTeX Error: Environment tikzpicture undefined.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.3 \begin{tikzpicture}
+                       
+Your command was ignored.
+Type  I <command> <return>  to replace it with another command,
+or  <return>  to continue without it.
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.4   [
+       scale=0.8,line width=.8pt,
+You're in trouble here.  Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+Missing character: There is no [ in font nullfont!
+Missing character: There is no s in font nullfont!
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+! Undefined control sequence.
+l.7       mark=at position 0.25 with {\arrow
+                                            [line width=1pt]{>}},
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no [ in font nullfont!
+Missing character: There is no l in font nullfont!
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+Missing character: There is no n in font nullfont!
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+Missing character: There is no p in font nullfont!
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+Missing character: There is no t in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no 0 in font nullfont!
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+Missing character: There is no w in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no h in font nullfont!
+! Undefined control sequence.
+l.9       mark=at position 0.75 with {\arrow
+                                            [line width=1pt]{>}}
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no [ in font nullfont!
+Missing character: There is no l in font nullfont!
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+Missing character: There is no t in font nullfont!
+Missing character: There is no ] in font nullfont!
+Missing character: There is no > in font nullfont!
+Missing character: There is no ] in font nullfont!
+! Undefined control sequence.
+l.12   \draw
+             [help lines,->] (-4,0) -- (4,0) coordinate (xaxis);
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no [ in font nullfont!
+Missing character: There is no h in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no > in font nullfont!
+Missing character: There is no ] in font nullfont!
+Missing character: There is no ( in font nullfont!
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+Missing character: There is no , in font nullfont!
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+Missing character: There is no ) in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no 4 in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no ) in font nullfont!
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+Missing character: There is no r in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no i in font nullfont!
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+Missing character: There is no t in font nullfont!
+Missing character: There is no e in font nullfont!
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+Missing character: There is no i in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no ; in font nullfont!
+! Undefined control sequence.
+l.13   \draw
+             [help lines,->] (0,-1)coordinate(-yaxis) -- (0,4) coordinate (y...
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no [ in font nullfont!
+Missing character: There is no h in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no l in font nullfont!
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+Missing character: There is no s in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no > in font nullfont!
+Missing character: There is no ] in font nullfont!
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+Missing character: There is no - in font nullfont!
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+Missing character: There is no ) in font nullfont!
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+Missing character: There is no o in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no y in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no x in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no 4 in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no y in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no x in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no ; in font nullfont!
+! Undefined control sequence.
+l.14   \node
+              at (1.5,-0.5) {$\bullet$};
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no 1 in font nullfont!
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+Missing character: There is no , in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no 5 in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no ; in font nullfont!
+! Undefined control sequence.
+l.15   \node
+              at (-1.5,-0.5) {$\bullet$};
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no 1 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no 5 in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no 5 in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no ; in font nullfont!
+! Undefined control sequence.
+l.16   \draw
+             [postaction=decorate] (3,0) arc (0:180:3) ;
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no [ in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no = in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no ] in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no 3 in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no : in font nullfont!
+Missing character: There is no 1 in font nullfont!
+Missing character: There is no 8 in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no : in font nullfont!
+Missing character: There is no 3 in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no ; in font nullfont!
+! Undefined control sequence.
+l.18   \draw
+             [postaction=decorate] (-3,0) --(3,0) ;
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no [ in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no = in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no ] in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no 3 in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no 3 in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no ; in font nullfont!
+! Undefined control sequence.
+l.19   \node
+             [below] at (xaxis) {$k_0$};
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no [ in font nullfont!
+Missing character: There is no b in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no w in font nullfont!
+Missing character: There is no ] in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no x in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no x in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no ; in font nullfont!
+! Undefined control sequence.
+l.20   \node
+             [above] at (yaxis) {$ik_0'$};
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no [ in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no b in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no v in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no ] in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no y in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no x in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no ; in font nullfont!
+! Undefined control sequence.
+l.27   \node
+             at (1.5,-0.95){$\scriptstyle (\omega_k-i\epsilon)$};
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no 1 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no 5 in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no 9 in font nullfont!
+Missing character: There is no 5 in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no ; in font nullfont!
+! Undefined control sequence.
+l.28   \node
+             at (-1.5,-0.95){$\scriptstyle -(\omega_k+i\epsilon)$};
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no 1 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no 5 in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no 9 in font nullfont!
+Missing character: There is no 5 in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no ; in font nullfont!
+! Undefined control sequence.
+l.29   \node
+             at (2,3.2){$x_0<0$};
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no 2 in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no 3 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no 2 in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no ; in font nullfont!
+
+! LaTeX Error: \begin{document} ended by \end{tikzpicture}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.30 \end{tikzpicture}
+                      
+Your command was ignored.
+Type  I <command> <return>  to replace it with another command,
+or  <return>  to continue without it.
+
+
+! LaTeX Error: Environment tikzpicture undefined.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.31 \begin{tikzpicture}
+                        
+Your command was ignored.
+Type  I <command> <return>  to replace it with another command,
+or  <return>  to continue without it.
+
+Missing character: There is no [ in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no = in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no 8 in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no y in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no = in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no 1 in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no w in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no h in font nullfont!
+Missing character: There is no = in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no 8 in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no = in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no k in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no g in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no k in font nullfont!
+Missing character: There is no = in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no 2 in font nullfont!
+Missing character: There is no 5 in font nullfont!
+Missing character: There is no w in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no h in font nullfont!
+! Undefined control sequence.
+l.35       mark=at position 0.25 with {\arrow
+                                             [line width=1pt]{>}},
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no [ in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no w in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no h in font nullfont!
+Missing character: There is no = in font nullfont!
+Missing character: There is no 1 in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no ] in font nullfont!
+Missing character: There is no > in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no k in font nullfont!
+Missing character: There is no = in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no 7 in font nullfont!
+Missing character: There is no 5 in font nullfont!
+Missing character: There is no w in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no h in font nullfont!
+! Undefined control sequence.
+l.37       mark=at position 0.75 with {\arrow
+                                             [line width=1pt]{>}}
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no [ in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no w in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no h in font nullfont!
+Missing character: There is no = in font nullfont!
+Missing character: There is no 1 in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no ] in font nullfont!
+Missing character: There is no > in font nullfont!
+Missing character: There is no ] in font nullfont!
+! Undefined control sequence.
+l.40   \draw
+             [help lines,->] (-4,0) -- (4,0) coordinate (xaxis);
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no [ in font nullfont!
+Missing character: There is no h in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no > in font nullfont!
+Missing character: There is no ] in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no 4 in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no 4 in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no x in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no x in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no ; in font nullfont!
+! Undefined control sequence.
+l.41   \draw
+             [help lines,->] (0,-1)coordinate(-yaxis) -- (0,4) coordinate (y...
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no [ in font nullfont!
+Missing character: There is no h in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no > in font nullfont!
+Missing character: There is no ] in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no 1 in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no y in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no x in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no 4 in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no y in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no x in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no ; in font nullfont!
+! Undefined control sequence.
+l.42   \node
+              at (1.5,-0.5) {$\bullet$};
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no 1 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no 5 in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no 5 in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no ; in font nullfont!
+! Undefined control sequence.
+l.43   \node
+              at (-1.5,-0.5) {$\bullet$};
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no 1 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no 5 in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no 5 in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no ; in font nullfont!
+! Undefined control sequence.
+l.44   \draw
+             [postaction=decorate] (3,0) arc (0:180:3) ;
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no [ in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no = in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no ] in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no 3 in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no : in font nullfont!
+Missing character: There is no 1 in font nullfont!
+Missing character: There is no 8 in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no : in font nullfont!
+Missing character: There is no 3 in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no ; in font nullfont!
+! Undefined control sequence.
+l.46   \draw
+             [postaction=decorate] (-3,0) --(3,0) ;
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no [ in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no = in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no ] in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no 3 in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no 3 in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no ; in font nullfont!
+! Undefined control sequence.
+l.47   \node
+             [below] at (xaxis) {$k_0$};
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no [ in font nullfont!
+Missing character: There is no b in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no w in font nullfont!
+Missing character: There is no ] in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no x in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no x in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no ; in font nullfont!
+! Undefined control sequence.
+l.48   \node
+             [above] at (-yaxis) {$ik_0'$};
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no [ in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no b in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no v in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no ] in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no y in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no x in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no ) in font nullfont!
+Missing character: There is no ; in font nullfont!
+! Undefined control sequence.
+l.49   \node
+             [below left] {$O$};
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no [ in font nullfont!
+Missing character: There is no b in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no w in font nullfont!
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+! Undefined control sequence.
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+
+! LaTeX Error: \begin{document} ended by \end{tikzpicture}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.58 \end{tikzpicture}
+                      
+Your command was ignored.
+Type  I <command> <return>  to replace it with another command,
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+
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+! LaTeX Error: \caption outside float.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.59 \caption
+             {Contornos de integración para el propagador retardado \label{...
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+
+! LaTeX Error: \begin{document} ended by \end{figure}.
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+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.60 \end{figure}
+                 
+Your command was ignored.
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+! LaTeX Error: Missing \begin{document}.
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+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.108 V
+       eamos las cantidades conservadas debido a la simetría de Poincaré d...
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+You're in trouble here.  Try typing  <return>  to proceed.
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+! LaTeX Error: Missing \begin{document}.
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+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.110 \begin{eqnarray}
+                      
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+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.115 E
+       l grupo de Poincaré tiene 10 dimensiones y sendas corrientes conserv...
+
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+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.117 L
+       as expresiones para las densidades de momentum lineal y angular del c...
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+! LaTeX Error: The font size command \normalsize is not defined:
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+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.118 
+      
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+l.118 
+      
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+l.118 
+      
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+l.118 
+      
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+l.118 
+      
+The control sequence at the end of the top line
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+l.118 
+      
+The control sequence at the end of the top line
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+                                                  }}
+l.118 
+      
+The control sequence at the end of the top line
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+l.118 
+      
+The control sequence at the end of the top line
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+l.118 
+      
+The control sequence at the end of the top line
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+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.119 \begin{eqnarray}
+                      
+You're in trouble here.  Try typing  <return>  to proceed.
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+
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+
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+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.124 C
+       onviene identificar las propiedades del tensor ${T^{\mu}}_{\nu}$ y la...
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+ []
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.126 L
+       a conservación del momentum lineal está garantizada cuando se anula...
+
+You're in trouble here.  Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+Missing character: There is no L in font nullfont!
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+
+Overfull \hbox (20.0pt too wide) in paragraph at lines 126--127
+[]
+ []
+
+
+Overfull \hbox (22.42477pt too wide) in paragraph at lines 126--127
+\OML/cmm/m/it/10 J[] \OT1/cmr/m/n/10 =
+ []
+
+
+Overfull \hbox (34.38326pt too wide) in paragraph at lines 126--127
+\OMS/cmsy/m/n/10 ^^@[][]\OML/cmm/m/it/10 ^^O[]$
+ []
+
+
+Overfull \hbox (22.42477pt too wide) in paragraph at lines 126--127
+\OML/cmm/m/it/10 J[] \OT1/cmr/m/n/10 =
+ []
+
+
+Overfull \hbox (57.18935pt too wide) in paragraph at lines 126--127
+\OMS/cmsy/m/n/10 ^^@[]\OML/cmm/m/it/10 x[]![]$ 
+ []
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.128 T
+       enemos
+You're in trouble here.  Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+Missing character: There is no T in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no s in font nullfont!
+
+Overfull \hbox (20.0pt too wide) in paragraph at lines 128--129
+[] 
+ []
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.130 \begin{eqnarray}
+                      
+You're in trouble here.  Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+
+Overfull \hbox (20.0pt too wide) in paragraph at lines 130--130
+[] 
+ []
+
+
+! LaTeX Error: Command \Box not provided in base LaTeX2e.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.132 \partial_{\mu}T^{\mu\nu} &=& -\left(\Box
+                                               + m^2\right)\phi~\partial^{\n...
+
+Load the latexsym or the amsfonts package to define this symbol
+
+
+Overfull \hbox (200.04205pt too wide) in alignment at lines 130--135
+ [][][] []
+ []
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.137 L
+       a conservación del momentum está garantizada por la ecuación de mo...
+
+You're in trouble here.  Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+Missing character: There is no L in font nullfont!
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+! Undefined control sequence.
+<write> ...ference `ecuacion.KG' on page \thepage 
+                                                  \space undefined\on@line .
+l.137 ...cuación de movimiento (\ref{ecuacion.KG}
+                                                  ) y la conservación del m...
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+
+LaTeX Warning: Reference `ecuacion.KG' on page  undefined on input line 137.
+
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+! Undefined control sequence.
+<write> ...: Reference `t.mu.nu' on page \thepage 
+                                                  \space undefined\on@line .
+l.137 ...se deriva de la expresión (\ref{t.mu.nu}
+                                                  ).
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+
+LaTeX Warning: Reference `t.mu.nu' on page  undefined on input line 137.
+
+Missing character: There is no ) in font nullfont!
+Missing character: There is no . in font nullfont!
+
+Overfull \hbox (20.0pt too wide) in paragraph at lines 137--138
+[]
+ []
+
+
+Overfull \hbox (10.86105pt too wide) in paragraph at lines 137--138
+[]
+ []
+
+
+Overfull \hbox (10.86105pt too wide) in paragraph at lines 137--138
+[] 
+ []
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.139 L
+       as componentes del vector densidad de momentum lineal (\ref{densidad....
+
+You're in trouble here.  Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+Missing character: There is no L in font nullfont!
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diff --git a/ejemplo_clase/seccion_campo_dirac.tex b/ejemplo_clase/seccion_campo_dirac.tex
new file mode 100644
index 0000000000000000000000000000000000000000..b728cf6515c62f8093c89e587657087136771eb2
--- /dev/null
+++ b/ejemplo_clase/seccion_campo_dirac.tex
@@ -0,0 +1,86 @@
+\chapter{Campo de Dirac}
+El Campo de Dirac es el objeto más importante en la descripción de partículas de espín $\frac{1}{2}$, fermiones. Partículas que obedecen la estadística de Fermi-Dirac. El desarrollo de esta parte sigue la forma de las referencias \cite{mandl2010quantum,peskin2018introduction}
+
+\section{Sobre la representación de número en fermiones}
+
+Un detalle a resaltar en la cuantización de una teoría de bosones es que el sistema libre es una colección de osciladores armónicos.
+
+Tenemos una serie de operadores de creación y destrucción de modos, etiquetados por estados, genéricamente $r,s \dots$
+
+\begin{eqnarray}
+	\label{algebra.creacion.destruccion.bosonica}
+	\comm{a_r}{a_s^{\dagger}} & = & \delta_{rs}, \nonumber\\
+	\comm{a_r}{a_s} & = & 0, \\
+	\comm{a_r^{\dagger}}{a_s^{\dagger}} & = & 0. \nonumber
+\end{eqnarray}
+
+El operador de número del estado $r$,
+
+\begin{eqnarray}
+	N_r & \equiv & a_r^{\dagger}a_r, \label{operador.numero.r} \\
+	\comm{N_{r}}{\opAdaga{s}} & = & \delta_{rs}\opAdaga{r} = \delta_{rs}\opAdaga{s}, \label{conmutador.operador.numero.r.aDaga}\\
+	\comm{N_{r}}{\opA{s}} &=& -\delta_{rs}\opA{r} = -\delta_{rs}\opA{s}, \label{conmutador.operador.numero.r.a}
+\end{eqnarray}
+
+cuenta el nivel (número de excitaciones o partículas) presentes en la configuración $r$. El operador $a_r^{\dagger}$ agrega una partícula de configuración $r$. Al contrario, el operador $a_r$ remueve una partícula.
+
+Existe un estado de vacío $\ket{0}$,
+
+\begin{equation}\label{aniquilacion.del.vacio}
+	a_r \ket{0} = 0;~~~\forall r.
+\end{equation}
+
+\begin{itemize}
+	\item
+	El vacío es el estado sin excitaciones (partículas) (ecuación \ref{aniquilacion.del.vacio})
+	\item
+	El vacío tiene la mínima energía del sistema: cero en la prescripción de orden normal.
+\end{itemize}
+
+Como hemos dicho, los operadores $\opAdaga{r}$ permiten ir agregando grados de libertad de partícula libre, con números cuánticos definidos por la etiqueta $r$ (4-momento lineal y espín) al estado sobre el cual actúan. En particular, podemos contabilizar que el nuevo estado ha modificado su 4-momento de conforme lo establecido en la etiqueta $r$.
+
+Por ejemplo, si consideramos el siguiente estado (sin normalizar):
+
+\begin{equation}
+	\opAdaga{\vec{p}}\opAdaga{\vec{p}}\opAdaga{\vec{p}~'}\ket{0} \sim \ket{\vec{p},\vec{p},\vec{p}~'},
+\end{equation}
+esperamos que represente un estado compuesto por 3 partículas libres. 2 de momento lineal $\vec{p}$ y una de momento lineal $\vec{p}~'$. Vamos a jurungar\footnote{tr. coloq. {\it R. Dom. y Ven.} hurgar \cite{asale_2021}} un poco este estado, para convencernos y entender mejor la idea.
+
+Aplicando el operador $N_{\vec{p}}=\opAdaga{\vec{p}}\opA{\vec{p}}$ nos queda:
+
+\begin{align*}
+	\renewcommand{\arraystretch}{1.75}
+	N_{\vec{p}}\ket{2\vec{p},\vec{p}~'} &\sim \opAdaga{\vec{p}}\opA{\vec{p}}~\opAdaga{\vec{p}}\opAdaga{\vec{p}}\opAdaga{\vec{p}~'}\ket{0} \\
+	&= \opAdaga{\vec{p}}~(\opAdaga{\vec{p}}\opA{\vec{p}} + [\opA{\vec{p}}~,~\opAdaga{\vec{p}}])~\opAdaga{\vec{p}}\opAdaga{\vec{p}~'}\ket{0} & ([\opA{\vec{p}}~,~\opAdaga{\vec{p}}]=1)\\
+	&= \opAdaga{\vec{p}}~(\opAdaga{\vec{p}}\opA{\vec{p}})~\opAdaga{\vec{p}}\opAdaga{\vec{p}~'}\ket{0} + \opAdaga{\vec{p}}\opAdaga{\vec{p}}\opAdaga{\vec{p}~'}\ket{0} \\
+	&= \opAdaga{\vec{p}}\opAdaga{\vec{p}}~(\opAdaga{\vec{p}}\opA{\vec{p}} + [\opA{\vec{p}}~,~\opAdaga{\vec{p}}])~\opAdaga{\vec{p}~'}\ket{0} + \opAdaga{\vec{p}}\opAdaga{\vec{p}}\opAdaga{\vec{p}~'}\ket{0} \\
+	&= \opAdaga{\vec{p}}\opAdaga{\vec{p}}~(\opAdaga{\vec{p}}\opA{\vec{p}})~\opAdaga{\vec{p}~'}\ket{0} + 2\opAdaga{\vec{p}}\opAdaga{\vec{p}}\opAdaga{\vec{p}~'}\ket{0} \\
+	&= \opAdaga{\vec{p}}\opAdaga{\vec{p}}\opAdaga{\vec{p}}~(\opAdaga{\vec{p}~'}\opA{\vec{p}} + [\opA{\vec{p}}~,~\opAdaga{\vec{p}~'}])~\ket{0} + 2\opAdaga{\vec{p}}\opAdaga{\vec{p}}\opAdaga{\vec{p}~'}\ket{0} & ([\opA{\vec{p}}~,~\opAdaga{\vec{p}~'}]=0) \\
+	&= \opAdaga{\vec{p}}\opAdaga{\vec{p}}\opAdaga{\vec{p}}~(\opAdaga{\vec{p}~'}\opA{\vec{p}})~\ket{0} + 2\opAdaga{\vec{p}}\opAdaga{\vec{p}}\opAdaga{\vec{p}~'}\ket{0} & (\opA{\vec{p}}~\ket{0}=0) \\
+	&= 2\opAdaga{\vec{p}}\opAdaga{\vec{p}}\opAdaga{\vec{p}~'}\ket{0} \\
+	&\sim 2\ket{2\vec{p},\vec{p}~'}.
+\end{align*}
+
+El autovalor del operador número de partículas de momento lineal $\vec{p}$ es 2. El estado contiene dos partículas de momento lineal $\vec{p}$.
+
+Se puede obtener el mismo resultado usando las propiedades del operador de número (\ref{conmutador.operador.numero.r.aDaga} y \ref{conmutador.operador.numero.r.a}). Probando para $N_{\vec{p}~'}$,
+
+\begin{align*}
+	\renewcommand{\arraystretch}{1.75}
+	N_{\vec{p}~'}\ket{2\vec{p},\vec{p}~'} &\sim N_{\vec{p}~'}\opAdaga{\vec{p}}\opAdaga{\vec{p}}\opAdaga{\vec{p}~'}\ket{0} & (\comm{N_{\vec{p}~'}}{\opAdaga{\vec{p}}~} = 0) \\
+	&= \opAdaga{\vec{p}}\opAdaga{\vec{p}}N_{\vec{p}~'}\opAdaga{\vec{p}~'}\ket{0} \\
+	&= \opAdaga{\vec{p}}\opAdaga{\vec{p}}~(\opAdaga{\vec{p}~'}N_{\vec{p}~'} + \comm{N_{\vec{p}~'}}{\opAdaga{\vec{p}~'}})\ket{0} & (\comm{N_{\vec{p}~'}}{\opAdaga{\vec{p}~'}} = \opAdaga{\vec{p}~'}) \\
+	&= \opAdaga{\vec{p}}\opAdaga{\vec{p}}\opAdaga{\vec{p}~'}N_{\vec{p}~'} \ket{0} + \opAdaga{\vec{p}}\opAdaga{\vec{p}}\opAdaga{\vec{p}~'}\ket{0} & (N_{\vec{p}~'} \ket{0} = 0) \\
+	&= \opAdaga{\vec{p}}\opAdaga{\vec{p}}\opAdaga{\vec{p}~'}\ket{0} \\
+	&\sim \ket{2\vec{p},\vec{p}~'}.
+	\end{align*}
+	
+El autovalor del operador número de partículas de momento lineal $\vec{p}~'$ es 1. El estado contiene una partícula de momento lineal $\vec{p}~'$.
+
+\section{Sobre la representación de número para fermiones}
+...
+
+\section{El Campo de Dirac}
+En la construcción de los ingredientes de una teoría de campos, la simetría de Poincaré juega un papel protagónico. La evidencia observacional y experimental accesible y que acumula nuestro conocimiento indica que esta simetría está presente a un nivel fundamental de la naturaleza y permite definir el conjunto de observadores inerciales.
+
+Los campos son objetos que dan cuenta de los grados de libertad en cierto sistema físico. En una teoría física exitosa, la forma general de estos objetos es independiente del observador que describe el sistema. Además, las transformaciones de simetría que relacionan a dos observadores relacionan también los campos presentes en la descripción de cada observador, transformándolos de forma que se pueden verificar las observaciones en cada sistema.
\ No newline at end of file
diff --git a/ejemplo_clase/seccion_campo_escalar.tex b/ejemplo_clase/seccion_campo_escalar.tex
new file mode 100644
index 0000000000000000000000000000000000000000..47d2b76b643828acdffb00ba579df06fccd94d4e
--- /dev/null
+++ b/ejemplo_clase/seccion_campo_escalar.tex
@@ -0,0 +1,129 @@
+Consideramos el campo escalar en sus versiones real y complejo. Para comenzar, introducimos la acción del campo escalar real:
+\begin{equation}\label{accion.campo.escalar.real}
+\mathcal{S}=\int {\rm d}^4 x \mathcal{L}=-\frac{1}{2}\int {\rm d}^4 x \left(\partial_{\mu}\phi\partial^{\mu}\phi - m^2\phi^2\right).
+\end{equation}
+
+El funcional $\mathcal{S}$ se hace extremo si el campo $\phi$ cumple la ecuación de Klein-Gordon,
+
+\begin{equation}\label{ecuacion.KG}
+\left(\Box + m^2\right)\phi=0.
+\end{equation}
+
+La ecuación (\ref{ecuacion.KG}) implica que el campo $\phi$ tiene soluciones de tipo onda plana, con una relación de dispersión de la forma $k^2=k^{\mu}k_{\mu}=m^2$. En la interpretación cuántica del campo de Klein-Gordon podremos decir que la onda plana de vector de onda $k_{\mu}$ corresponde al estado de una partícula de momentum lineal definido.
+
+Se puede hallar la solución más general de la ecuación (\ref{ecuacion.KG}), pasando al espacio de Fourier. Se puede escribir de la siguiente forma,
+
+\begin{equation}\label{solucion.KG.real.ondas.planas}
+\phi(x)=\int {\rm d}^3k(a(\vec{k})f_{\vec{k}}(x)+\bar{a}(\vec{k})\bar{f}_{\vec{k}}(x)),
+\end{equation}
+donde $a(\vec{k})$ es una función arbitraria y se han hecho las siguientes definiciones
+\begin{eqnarray}
+f_{\vec{k}}(x) &=& \frac{1}{(2\pi)^{3/2}\sqrt{2\omega_{k}}}\left.e^{-ik_{\mu}x^{\mu}}\right|_{k_0=\omega_k}, \\
+\omega_k &=& +\sqrt{m^2+|\vec{k}|^2}. \label{omega.k.KG}
+\end{eqnarray}
+
+La función $f_{\vec{k}}(x)$, con la definición de $\omega_k$ satisface la ecuación de Klein-Gordon. De igual forma lo hace la expresión (\ref{solucion.KG.real.ondas.planas}). Además, la normalización de las funciones $f_{\vec{k}}(x)$ garantiza que se cumplan las siguientes propiedades,
+\begin{eqnarray}
+(f_{\vec{k}},f_{\vec{k}'}) &=& \delta^3(\vec{k}-\vec{k}'), \\
+(\bar{f}_{\vec{k}},\bar{f}_{\vec{k}'}) &=& -\delta^3(\vec{k}-\vec{k}'), \\
+(f_{\vec{k}},\bar{f}_{\vec{k}'}) &=& 0,
+\end{eqnarray}
+donde se ha definido el paréntesis $(f_1,f_2)$ de la siguiente forma
+\iffalse
+\begin{equation}
+(f_1,f_2)=i\int {\rm d}^3x\bar{f}_1{\genfrac{}{}{0pt}{0}{\leftrightarrow}{\partial_{0}}}f_2.
+\end{equation}
+\fi
+\begin{eqnarray}
+\renewcommand*{\arraystretch}{0.8}
+(f_1,f_2) &=& i\int {\rm d}^3x\bar{f}_1{\begin{array}{c}
+\leftrightarrow \\
+\partial_{0}\\
+\\
+\end{array}
+}f_2\\
+ &=& i\int {\rm d}^3 x (\bar{f}_1\partial_{0}f_2 - (\partial_{0}\bar{f}_1)f_2).
+\end{eqnarray}
+
+Para construir soluciones particulares de la ecuación de Klein-Gordon se construye la función de Green, considerando la forma no-homogénea de la ecuación (\ref{ecuacion.KG})
+
+\begin{equation}\label{ecuacion.KG.con.fuentes}
+\left(\Box + m^2\right)\phi=\rho.
+\end{equation}
+
+Se define $G(x-x')$ tal que
+
+\begin{eqnarray}\label{ecuacion.propagador.KG.real}
+&& \left(\Box_x + m^2\right)G(x-x')=\delta^4(x-x'),\\
+&\Rightarrow & \phi(x) = \phi_H(x) + \int{\rm d}^4 x' G(x-x')\rho(x'),
+\end{eqnarray}
+donde $\phi_H(x)$ es solución de la ecuación homogénea (\ref{ecuacion.KG}).
+
+Como es acostumbrado se escribe la solución de la ecuación (\ref{ecuacion.propagador.KG.real}) en el espacio de Fourier,
+
+\begin{equation}
+\label{propagador.KG.fourier}
+G(x) = \frac{1}{(2\pi)^4}\int{\rm d}^4 k \left[\frac{-1}{k_0^2-\omega_k^2}\right]e^{-ikx},
+\end{equation}
+donde $\omega_k$ tiene la misma definición que en (\ref{omega.k.KG}).
+
+A partir de (\ref{propagador.KG.fourier}) se definen los propagadores retardado y avanzado según se defina el contorno de la integral en $k_0$. Por ejemplo, añadiendo una componente infinitesimal imaginaria negativa a las singularidades $k_0=\pm\omega_k$ se definirá el propagador retardado (fig \ref{contornos.propagador.retardado}),
+
+\begin{eqnarray}
+\label{propagador.KG.retardado}
+\Delta_{ret}(x) &=& \lim_{\epsilon\rightarrow 0}\frac{1}{(2\pi)^4}\int{\rm d}^4 k \left[\frac{-1}{(k_0+i\epsilon)^2-\omega_k^2}\right]e^{-ikx} \nonumber \\
+&=& \frac{\Theta(x_0)}{(2\pi)^3}\int{\rm d}^3 k~\frac{\sin{\omega_k x_0}}{\omega_k}~e^{i\vec{k}\cdot\vec{x}}.
+\end{eqnarray}
+
+Si en cambio la componente infinitesimal es positiva se define el propagador avanzado
+\begin{equation}
+\Delta_{av}(x) = \Delta_{ret}(-x).
+\end{equation}
+
+XXXXX
+
+
+%%%%
+\input{propagador_retardado.tex}
+%%%%
+
+Veamos las cantidades conservadas debido a la simetría de Poincaré de la acción (\ref{accion.campo.escalar.real}). La corriente conservada dependerá del tensor de energía-impulso (\ref{J.noether.general}, \ref{t.mu.nu.general}),
+
+\begin{eqnarray}
+J^{\mu} &=& -{T^{\mu}}_{\nu}\delta x^{\nu}, \\
+{T^{\mu}}_{\nu} &=& - \partial^{\mu}\phi\partial_{\nu}\phi - \delta^{\mu}_{\nu} \mathcal{L}. \label{t.mu.nu}
+\end{eqnarray}
+
+El grupo de Poincaré tiene 10 dimensiones y sendas corrientes conservadas independientes. Estas corrientes quedan empaquetadas en un vector y un tensor antisimétrico de dos índices.
+
+Las expresiones para las densidades de momentum lineal y angular del campo $\phi$ se obtienen definiendo $\delta x^{\nu}=\epsilon^{\nu}$ y $\delta x^{\nu}={\omega^{\nu}}_{\alpha}x^{\alpha}$ respectivamente. Los 4 parámetros $\epsilon$ corresponden a una traslación infinitesimal arbitraria y los $\omega$ cumplen $\omega_{\mu\nu}=-\omega_{\nu\mu}$, siendo los 6 parámetros independientes del grupo de Lorentz.
+
+\begin{eqnarray}
+p_{\nu} &=& -{T^{0}}_{\nu}, \label{densidad.P.KG.real}\\
+m^{\alpha\nu} &=& x^{[\alpha}p^{\nu]}. \label{densidad.J.KG.real}
+\end{eqnarray}
+
+Conviene identificar las propiedades del tensor ${T^{\mu}}_{\nu}$ y la conservación de la corriente de Noether.
+
+La conservación del momentum lineal está garantizada cuando se anula la divergencia de la corriente traslacional $J_{t}^{\mu}=-{T^{\mu}}_{\nu}\epsilon^{\nu}$. Por otro lado, la conservación del momento angular va emparejada con la anulación de la corriente rotacional $J_{r}^{\mu}=-{T^{\mu[\nu}}x^{\alpha]}\omega_{\nu\alpha}$.
+
+Tenemos
+
+\begin{eqnarray}
+\partial_{\mu}J_{t}^{\mu}=0 &\Longrightarrow &  \partial_{\mu}{T^{\mu}}_{\nu}=0, \nonumber \\
+\partial_{\mu}T^{\mu\nu} &=& -\left(\Box + m^2\right)\phi~\partial^{\nu}\phi. \\
+\partial_{\mu}J_{r}^{\mu}=0 &\Longrightarrow & \partial_{\mu}(T^{\mu[\nu}x^{\alpha]})=0, \nonumber \\
+\partial_{\mu}(T^{\mu[\nu}x^{\alpha]}) &=& x^{\alpha}\partial_{\mu}T^{\mu\nu} - x^{\nu}\partial_{\mu}T^{\mu\alpha} + 2~T^{[\alpha\nu]}.
+\end{eqnarray}
+
+La conservación del momentum está garantizada por la ecuación de movimiento (\ref{ecuacion.KG}) y la conservación del momento angular requiere además la propiedad de simetría del tensor de energía impulso que se deriva de la expresión (\ref{t.mu.nu}).
+
+Las componentes del vector densidad de momentum lineal (\ref{densidad.P.KG.real}) son las siguientes,
+
+\begin{eqnarray}
+p_{0} &=& \frac{1}{2}\left((\Pi^{0})^2+|\vec{\nabla}\phi|^2+m^2\phi^2\right), \label{densidad.P0.KG.real}\\
+\vec{p} &=& \Pi^{0}~\vec{\nabla}\phi, \label{densidad.P.espacial.KG.real}
+\end{eqnarray}
+donde como es usual $\Pi^{i\mu}=\frac{\partial\mathcal{L}}{\partial\partial_{\mu}\phi_{i}}$ (\ref{momento.lagrangiano.general}). Se evidencia que la parte temporal del vector densidad de momentum lineal es efectivamente la densidad hamiltoniana.
+
+