Gauge Properties of Conserved Currents in Abelian Versus Nonabelian Theories

TL;DR

This paper explores the fundamental differences in gauge properties of conserved currents between abelian and nonabelian theories, highlighting how self-coupling in nonabelian theories transforms gauge invariance characteristics.

Contribution

It clarifies the physical origin of gauge property differences and explains how nonabelian theories derive from abelian ones through self-coupling of conserved currents.

Findings

Nonabelian currents can be expressed as gauge invariants modulo superpotentials.

Self-coupling turns abelian conserved currents into superpotentials in nonabelian theories.

Discussion on the behavior of other conserved currents in these theories.

Abstract

We clarify the physical origin of the difference between gauge properties of conserved currents in abelian and nonabelian 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 1 and 2 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 non-invariantizable abelian conserved currents into (on-shell) superpotentials. The fate of other conserved currents is also discussed.