Connecting Green's Functions in an Arbitrary Pair of Gauges and an Application to Planar Gauges

TL;DR

This paper develops a method to connect Green's functions across different gauges in Yang-Mills theory using finite field-dependent BRS transformations, enabling consistent comparisons of gauge-dependent quantities.

Contribution

It introduces a finite field-dependent BRS transformation that relates Green's functions in arbitrary gauge pairs, including planar gauges, while preserving gauge-invariant observables.

Findings

Established a gauge connection for Green's functions via BRS transformations.

Derived relations between Green's functions in different gauges.

Applied the method to planar and Lorentz gauges.

Abstract

We establish a finite field-dependent BRS transformation that connects the Yang-Mills path-integrals with Faddeev-Popov effective actions for an arbitrary pair of gauges F and F'. We establish a result that relates an arbitrary Green's function [either a primary one or one that of an operator] in an arbitrary gauge F' to those in gauge F that are compatible to the ones in gauge F by its construction [in that the construction preserves expectation values of gauge-invariant observables]. We establish parallel results also for the planar gauge-Lorentz gauge connection.