Integral equation for gauge invariant quark Green's function

TL;DR

This paper derives an integral equation for gauge invariant quark Green's functions with phase factors along straight lines, involving Wilson loops with skew-polygonal contours, advancing the understanding of nonperturbative QCD effects.

Contribution

It introduces a novel integral equation for gauge invariant quark Green's functions using skew-polygonal phase factors and relates kernels to Wilson loops with functional derivatives.

Findings

Derived an integral equation for the quark Green's function with straight-line phase factors.

Connected kernels to Wilson loops with skew-polygonal contours and functional derivatives.

Provided a framework for analyzing gauge invariant Green's functions in QCD.

Abstract

We consider gauge invariant quark two-point Green's functions in which the gluonic phase factor follows a skew-polygonal line. Using a particular representation for the quark propagator in the presence of an external gluon field, functional relations between Green's functions with different numbers of segments of the polygonal lines are established. An integral equation is obtained for the Green's function having a phase factor along a single straight line. The related kernels involve Wilson loops with skew-polygonal contours and with functional derivatives along the sides of the contours.