= Stress-energy tensor improvement
{title2=$T\prime{}^{\mu\nu}=T^{\mu\nu}+\partial_\rho B^{\rho\mu\nu}$}
Adding $\partial_\rho B^{\rho\mu\nu}$ with $B^{\rho\mu\nu}=-B^{\mu\rho\nu}$ to a <stress-energy tensor> preserves its divergence identically, since commuting partial derivatives annihilates the antisymmetric pair. The total <four-momentum> changes only by a spatial boundary term. Improvements can make local densities symmetric or <gauge-invariant>; equality of integrated charges requires the chosen <boundary conditions>. Equation-of-motion terms can also relate representatives <on shell>.
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