= Canonical stress-energy tensor of the Maxwell field
{title2=$T^{\mu\nu}=-F^{\mu\rho}\partial^\nu A_\rho+\frac14\eta^{\mu\nu}F_{\rho\sigma}F^{\rho\sigma}$}
For signature $(+,-,-,-)$, translation invariance of the <Maxwell Lagrangian> gives this tensor. It is generally neither symmetric nor gauge invariant. The <antisymmetric superpotential improvement> $-\partial_\rho(F^{\rho\mu}A^\nu)$ produces, on the source-free equations of motion, the symmetric <electromagnetic stress-energy tensor> $\Theta^{\mu\nu}=-F^{\mu\rho}F^\nu{}_{\rho}+\eta^{\mu\nu}F^2/4$, which is traceless in four spacetime dimensions.
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