On Gauge Invariance and Ward Identities for the Wilsonian Renormalisation Group

TL;DR

This paper explores gauge invariance in non-Abelian gauge theories using the Wilsonian Renormalisation Group, deriving the beta-function and demonstrating the compatibility of modified Ward identities with the flow.

Contribution

It introduces a modified Ward identity in the Wilsonian RG framework and shows its compatibility with the flow, deriving the universal 1-loop beta-function.

Findings

Modified Ward identity is compatible with the flow.

Full effective action satisfies the usual Ward identity.

Universal 1-loop beta-function derived.

Abstract

We investigate non-Abelian gauge theories within a Wilsonian Renormalisation Group approach. The cut-off term inherent in this approach leads to a modified Ward identity (mWI). It is shown that this mWI is compatible with the flow and that the full effective action satisfies the usual Ward identity (WI). The universal 1-loop beta-function is derived within this approach and the extension to the 2-loop level is briefly outlined.