\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}