Particles with non abelian charges

TL;DR

This paper presents a method using Grassmann variables and a U(1) gauge field with a Chern-Simons term to efficiently describe non-abelian charges in worldline quantum field theory, simplifying calculations of amplitudes.

Contribution

It introduces a novel approach coupling Grassmann variables with a U(1) gauge field and Chern-Simons term to project onto irreducible non-abelian representations.

Findings

Tested on scalar and spin 1/2 contributions to gluon self-energy

Method simplifies analysis of non-abelian charges in worldline approaches

Potential to streamline complex amplitude calculations

Abstract

Efficient methods for describing non abelian charges in worldline approaches to QFT are useful to simplify calculations and address structural properties, as for example color/kinematics relations. Here we analyze in detail a method for treating arbitrary non abelian charges. We use Grassmann variables to take into account color degrees of freedom, which however are known to produce reducible representations of the color group. Then we couple them to a U(1) gauge field defined on the worldline, together with a Chern-Simons term, to achieve projection on an irreducible representation. Upon gauge fixing there remains a modulus, an angle parametrizing the U(1) Wilson loop, whose dependence is taken into account exactly in the propagator of the Grassmann variables. We test the method in simple examples, the scalar and spin 1/2 contribution to the gluon self energy, and suggest that it might simplify the analysis of more involved amplitudes.