Worldline colour fields and non-Abelian quantum field theory

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 $SU(N)$.

Comments: 10 pages. To appear in Proceedings of the 6th International Conference on New Frontiers in Physics (ICNFP 2017), published by European Physical Journal Web of Conferences