Using gauge invariance to symmetrize the energy-momentum tensor of electrodynamics

Abstract

It is shown that using Noether's Theorem explicitly employing gauge invariance for variations of the electromagnetic four-potential $A^\mu$ straightforwardly ensures that the resulting electromagnetic energy-momentum tensor is symmetric. The Belinfante symmetrization procedure is not necessary. The method is based on Bessel-Hagen's 1921 clarification of Noether's original procedure, suggesting that the symmetry problem arises from an incomplete implementation of Noether's Theorem.