Radial propagators and Wilson loops

TL;DR

This paper establishes a relation between the radial gauge propagator and Wilson loops, revealing divergence issues and proposing a regularization scheme, thereby advancing calculations in gauge theories.

Contribution

It introduces a novel relation connecting the radial gauge propagator with Wilson loops and offers a regularization method for loop calculations.

Findings

Radial gauge propagator diverges in four dimensions for free fields.

The divergence is explained via Wilson loop renormalization properties.

A new regularization scheme for loop calculations is proposed.

Abstract

We present a relation which connects the propagator in the radial (Fock-Schwinger) gauge with a gauge invariant Wilson loop. It is closely related to the well-known field strength formula and can be used to calculate the radial gauge propagator. The result is shown to diverge in four-dimensional space even for free fields, its singular nature is however naturally explained using the renormalization properties of Wilson loops with cusps and self-intersections. Using this observation we provide a consistent regularization scheme to facilitate loop calculations. Finally we compare our results with previous approaches to derive a propagator in Fock-Schwinger gauge.