Relating Green's Functions in Axial and Lorentz Gauges using Finite Field-Dependent BRS Transformations

TL;DR

This paper introduces a method using finite field-dependent BRS transformations to relate Green's functions across different gauge choices, specifically Lorentz and axial gauges, facilitating calculations in gauge theories.

Contribution

The paper develops a novel approach to connect Green's functions in different gauges using finite field-dependent BRS transformations, applicable to operator functions and derived from infinitesimal transformations.

Findings

Green's functions in axial gauge expressed as series in Lorentz gauge functions

Method applicable to operator Green's functions

Potential applications in gauge theory calculations

Abstract

We use finite field-dependent BRS transformations (FFBRS) to connect the Green functions in a set of two otherwise unrelated gauge choices. We choose the Lorentz and the axial gauges as examples. We show how the Green functions in axial gauge can be written as a series in terms of those in Lorentz gauges. Our method also applies to operator Green's functions. We show that this process involves another set of related FFBRS transfomations that is derivable from infinitesimal FBRS. We suggest possible applications.