Wilson Loop and the Treatment of Axial Gauge Poles

TL;DR

This paper investigates the gauge invariance of the Wilson loop using a new axial gauge propagator treatment based on finite field-dependent BRS transformations, demonstrating invariance at specific orders and preserving thermal Wilson loops.

Contribution

It introduces a novel approach to axial gauge propagator treatment that ensures gauge invariance of Wilson loops using FFBRS transformations.

Findings

Wilson loop invariance verified to O(g^4)

Thermal Wilson loop preserved to O(g^2)

Prescription maintains gauge invariance automatically

Abstract

We consider the question of gauge invariance of the Wilson loop in the light of a new treatment of axial gauge propagator proposed recently based on a finite field-dependent BRS (FFBRS) transformation. We remark that as under the FFBRS transformation the vacuum expectation value of a gauge invariant observable remains unchanged, our prescription automatically satisfies the Wilson loop criterion. Further, we give an argument for {\it direct} verification of the invariance of Wilson loop to O(g^4) using the earlier work by Cheng and Tsai. We also note that our prescription preserves the thermal Wilson loop to O(g^2).