Maxwell方程式 \begin{align} \partial_{\nu}F^{\nu\mu} = J^{\mu} \end{align} Lorentz変換のもとでは \begin{align} &L_{\nu}^{\;\lambda}\partial_{\lambda} L^{\nu}_{\;\sigma}L^{\mu}_{\;\epsilon}F^{\sigma\epsilon} = L^{\mu}_{\;\epsilon} J^{\epsilon} \\ \leftrightarrow & L_{\nu}^{\;\lambda} L^{\nu}_{\;\sigma} \partial_{\lambda} F^{\sigma\mu} = J^{\mu} \\ \leftrightarrow & g^{\lambda}_{\;\sigma} \partial_{\lambda} F^{\sigma\mu} = J^{\mu}\\ \leftrightarrow & \partial_{\lambda}F^{\lambda\mu} = J^{\mu} \end{align}

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Maxwell方程式のLorentz不変性