Field-Dependent BRS Tranformations and Correct Prescription for 1/(n.k)^p-Type Singularities in Axial Gauges

TL;DR

This paper introduces a novel method using finite field-dependent BRS transformations to handle singularities in axial gauge boson propagators, providing a consistent prescription within the path-integral formalism.

Contribution

It develops an alternative approach to treat 1/(n.k)^p singularities in axial gauges by interpolating from Lorentz gauges using BRS transformations.

Findings

Derives an psilon-dependent tree propagator in axial gauges.

Provides a consistent prescription for singularities in axial gauge propagators.

Connects axial and Lorentz gauges through BRS transformations.

Abstract

The axial-gauge boson propagator contains 1/(n.k)^p-type singularities. These singularities have generally been treated by inventing prescriptions for them. We propose an alternative procedere for treating these singularities in the path-integral formalism using the known way of treating the 1/k^{2n}-type singularities in Lorentz-type gauges. For this purpose we use a finite field-dependent BRS transformation that inerpolates between the Lorentz and axial-type gauges. We arrive at the \epsilon-dependent tree propagator in axial-type gauges.