= Gauge-covariant time translation
{title2=$\delta A_\nu=\alpha F_{0\nu}$}
For the <Maxwell field>, the variation $\delta A_\nu=\alpha F_{0\nu}=\alpha(\partial_0A_\nu-\partial_\nu A_0)$ is time translation combined with a <gauge transformation>. With constant $\alpha$, $\delta F_{\mu\nu}=\alpha\partial_0F_{\mu\nu}$, and the Lagrangian changes by $\alpha\partial_0\mathcal L$. Its <Noether current> is directly the time component of the <gauge-invariant Maxwell stress-energy tensor>, providing the physical energy density without a potential-dependent improvement step.
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