<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\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 &amp; \equiv &amp; \sum_i\partial_i^2 \\
\square &amp; \equiv &amp; \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}}&amp;=&amp;\Pi^{i\mu}\delta\phi_i-{T^{\mu}}_{\nu}\delta x^{\nu}, \\
{J^{\mu}}_{I}&amp;=&amp;\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} &amp;=&amp; \frac{\partial x^{\nu}}{\partial\epsilon^{I}}\delta\epsilon^{I}, \\
\delta\phi_i &amp;=&amp; \frac{\partial\phi_i}{\partial\epsilon^{I}}\delta\epsilon^{I}, \\
\Pi^{i\mu} &amp;=&amp; \frac{\partial\mathcal{L}}{\partial\partial_{\mu}\phi_{i}}, \label{momento.lagrangiano.general}\\
{T^{\mu}}_{\nu} &amp;=&amp; \Pi^{i\mu}\partial_{\nu}\phi_{i} - \delta^{\mu}_{\nu} \mathcal{L}.\label{t.mu.nu.general}
\end{eqnarray}


\end{itemize}</pre></body></html>