A Primer for Manifestly Gauge Invariant Computations in SU(N) Yang-Mills

TL;DR

This paper presents a gauge-invariant method for performing continuum computations in SU(N) Yang-Mills theory using the Exact Renormalisation Group, avoiding gauge fixing and scheme details, and demonstrates its application in calculating the two-loop beta function.

Contribution

It refines diagrammatic techniques enabling gauge-invariant continuum calculations in SU(N) Yang-Mills theory without fixing gauges or regularisation details.

Findings

Successfully computed the two-loop beta function using the method.

Demonstrated the effectiveness of gauge-invariant techniques in complex calculations.

Provided a framework for higher-loop computations without gauge fixing.

Abstract

It has recently been determined that, within the framework of the Exact Renormalisation Group, continuum computations can be performed to any loop order in SU(N) Yang-Mills theory without fixing the gauge or specifying the details of the regularisation scheme. In this paper, we summarise and refine the powerful diagrammatic techniques which facilitate this procedure and illustrate their application in the context of a calculation of the two-loop beta function.