Antisymmetric superpotential improvement ($T^{\mu \nu }\mapsto T^{\mu \nu }+{\partial }_{\rho }{B}^{\rho \mu \nu }$)

If $B^{\rho \mu \nu }=-B^{\mu \rho \nu }$, commuting partial derivatives gives ${\partial }_{\mu }{\partial }_{\rho }{B}^{\rho \mu \nu }=0$. Such an improvement preserves conservation of a stress-energy tensor and changes integrated charges only by a spatial boundary term. The Belinfante-Rosenfeld stress-energy tensor is obtained through this type of improvement.