Correct Treatment of 1/(\eta\cdot k)^p Singularities in the Axial Gauge Propagator

TL;DR

This paper introduces a new method for handling singularities in axial gauge propagators by using a finite field-dependent BRS transformation, resulting in a propagator free of spurious poles.

Contribution

It proposes an alternative to prescriptions for singularities in axial gauges by interpolating from Lorentz gauges using BRS transformations, leading to a well-behaved propagator.

Findings

The constructed propagator has no spurious poles for real momenta.

The propagator's complex structure near tak=0 can be simplified.

The method provides a consistent treatment of singularities in axial gauges.

Abstract

The propagators in axial-type, light-cone and planar gauges contain 1/(\eta\cdot k)^p-type singularities. These singularities have generally been treated by inventing prescriptions for them. In this work, we propose an alternative procedure for treating these singularities in the path integral formalism using the known way of treating the singularities in Lorentz gauges. To this end, we use a finite field-dependent BRS transformation that interpolates between Lorentz-type and the axial-type gauges. We arrive at the $\epsilon$-dependent tree propagator in the axial-type gauges. We examine the singularity structure of the propagator and find that the axial gauge propagator so constructed has {\it no} spurious poles (for real $k$). It however has a complicated structure in a small region near $\eta\cdot k=0$. We show how this complicated structure can effectively be replaced by a much simpler propagator.