Flow Equations for Yang-Mills Theories in General Axial Gauges

TL;DR

This paper develops a Wilsonian Renormalisation Group approach for non-Abelian gauge theories in axial gauges, avoiding divergences and maintaining gauge invariance, with potential for non-perturbative analysis.

Contribution

It introduces a novel formulation of Yang-Mills theories in axial gauges using flow equations that prevent divergences and preserve gauge invariance, providing a basis for non-perturbative studies.

Findings

No spurious divergences in axial gauges using flow equations

Axial gauge condition is a fixed point of the flow

Modified Ward identities ensure gauge invariance

Abstract

We present a formulation of non-Abelian gauge theories in general axial gauges using a Wilsonian (or 'Exact') Renormalisation Group. No 'spurious' propagator divergencies are encountered in contrast to standard perturbation theory. Modified Ward identities, compatible with the flow equation, ensure gauge invariance of physical Green functions. The axial gauge $n A=0$ is shown to be a fixed point under the flow equation. Possible non-perturbative approximation schemes and further applications are outlined.