Abelian Fock-Schwinger representation for the quark propagator in external gauge field

TL;DR

This paper develops an Abelian representation of the non-Abelian Wilson loop and quark propagator in external gauge fields, extending existing approaches to open curves and non-compact groups for better analytical tools.

Contribution

It introduces a novel Abelian form of the Schwinger-Fock representation for the quark propagator in external gauge fields, expanding the Diakonov-Petrov approach.

Findings

Derived Abelian form of the Wilson loop for open curves

Extended Abelian representation to non-compact groups

Provided new analytical expressions for quark propagator

Abstract

We develop the Diakonov-Petrov approach to the representation of the non-Abelian Wilson loop in an Abelian form. First of all, we extend this approach to the Abelian representation of the parallel transporter corresponding to the open curve rather than to the closed contour. Next, we extend this representation to the case of the non-compact groups. The obtained expressions allow to derive the Abelian form of the Schwinger-Fock representation for the quark propagator in an external color gauge field.