Gauge Properties of Conserved Currents in Abelian Versus Non-abelian Theories

Abstract

We clarify the physical origin of the difference between gauge properties of conserved currents in Abelian and non-Abelian theories. In the latter, but not in the former, such currents can always be written on-shell as gauge invariants modulo identically conserved, superpotential, terms. For the “isotopic” vector and the stress tensor currents of spins one and two respectively, we explain this difference by the fact that the non-Abelian theories are just the self-coupled versions of the Abelian ones using these currents as sources. More precisely, we indicate how the self-coupling turns the noninvariantizable Abelian conserved currents into (on-shell) superpotentials. The fate of other conserved currents is also discussed.