Non-abelian gauge theories as a consequence of perturbative quantum gauge invariance

TL;DR

This paper demonstrates that non-abelian gauge theories, specifically Yang-Mills theories, naturally arise from the principle of perturbative quantum gauge invariance in the context of massless vector bosons.

Contribution

It shows that the structure of Yang-Mills theories can be derived solely from perturbative quantum gauge invariance, revealing the fundamental origin of non-abelian gauge interactions.

Findings

Yang-Mills structure emerges automatically from gauge invariance

Couplings are constrained to be of Yang-Mills type plus divergence- and coboundary couplings

Method extends to massive gauge theories

Abstract

We show for the case of interacting massless vector bosons, how the structure of Yang-Mills theories emerges automatically from a more fundamental concept, namely perturbative quantum gauge invariance. It turns out that the coupling in a non-abelian gauge theory is necessarily of Yang-Mills type plus divergence- and coboundary couplings. The extension of the method to massive gauge theories is briefly discussed.