= Gauge-invariant Maxwell stress-energy tensor
{title2=$\Theta^{\mu\nu}$}
In signature $+---$, the <Maxwell Lagrangian> yields
$$
\Theta^\mu{}_{\nu}=-F^{\mu\rho}F_{\nu\rho}+\tfrac14\delta^\mu{}_{\nu}F_{\rho\sigma}F^{\rho\sigma}.
$$
It is symmetric after raising its second index, <gauge-invariant>, and conserved on the source-free <Maxwell equations>. Its energy density is $\frac12(\mathbf E^2+\mathbf B^2)$ and its energy flux is the <Poynting vector>. Its difference from the <canonical stress-energy tensor> is an antisymmetric superpotential divergence plus an equation-of-motion term, so integrated charges coincide when the constraints and vanishing boundary terms are imposed.
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