On Gauge Invariant Wilsonian Flows

TL;DR

This paper explores how to implement gauge-invariant Wilsonian renormalization flows in non-Abelian gauge theories, highlighting differences between quantum and thermal fluctuations and proposing solutions for gauge invariance.

Contribution

It demonstrates that a fully gauge-invariant Wilsonian flow can be achieved for thermal fluctuations, addressing a key challenge in gauge theory renormalization.

Findings

Gauge invariance is incompatible with Wilsonian coarse-graining in quantum fluctuations.

A fully gauge-invariant flow can be constructed for thermal fluctuations.

The approach advances the understanding of gauge-invariant renormalization group methods.

Abstract

We investigate non-Abelian gauge theories within a Wilsonian Renormalisation Group approach. Our main question is: How close can one get to a gauge invariant flow, despite the fact that a Wilsonian coarse-graining seems to be incompatible with gauge invariance? We discuss the possible options in the case of quantum fluctuations, and argue that for thermal fluctuations a fully gauge invariant implementation can be obtained.