Worldline colour fields and non-Abelian quantum field theory

TL;DR

This paper explores a worldline approach to non-Abelian quantum field theory, incorporating colour degrees of freedom via worldline colour fields, analyzing its supersymmetry, and demonstrating quantization methods.

Contribution

It introduces a locally supersymmetric worldline theory with colour fields for non-Abelian gauge groups and details its canonical quantization and path integral formulation.

Findings

Constructed a supersymmetric worldline theory with colour fields

Analyzed the constraint algebra and supersymmetry properties

Demonstrated quantization and path integral on $S^{1}$ for $SU(N)$ representations

Abstract

In the worldline approach to non-Abelian field theory the colour degrees of freedom of the coupling to the gauge potential can be incorporated using worldline "colour" fields. The colour fields generate Wilson loop interactions whilst Chern-Simons terms project onto an irreducible representation of the gauge group. We analyse this augmented worldline theory in phase space focusing on its supersymmetry and constraint algebra, arriving at a locally supersymmetric theory in superspace. We demonstrate canonical quantisation and the path integral on $S^{1}$ for simple representations of $SU(N)$.