= Gauge-compensated time translation in electromagnetism
{title2=$\delta A_\nu=\alpha F_{0\nu}$}
With signature $(+,-,-,-)$ and $\mathcal L=-F_{\mu\nu}F^{\mu\nu}/4$, combine a time translation $\alpha\partial_0A_\nu$ with the <gauge transformation> of parameter $-\alpha A_0$. Its <Noether current> is $J^\mu=-F^{\mu\nu}F_{0\nu}-\delta^\mu_0\mathcal L$, the gauge-invariant energy current. The density is $(|\mathbf E|^2+|\mathbf B|^2)/2$. On the source-free field equations it differs from the canonical translation current by $\partial_\nu(A_0F^{\mu\nu})$, an antisymmetric superpotential divergence, so total energies agree when the boundary term vanishes.
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