Stress-energy superpotential ($B^{\rho \mu \nu }=-B^{\mu \rho \nu }$)

A stress-energy superpotential is an antisymmetric tensor $B^{\rho \mu \nu }=-B^{\mu \rho \nu }$ whose divergence supplies a stress-energy tensor improvement. In the Maxwell field, the potential-dependent expression $B^{\rho \mu }{}_{\nu }=F^{\mu \rho }{A}_{\nu }$ produces the difference between canonical and gauge-invariant stress-energy tensors on shell. Antisymmetry ensures identically conserved improvement terms.