A Derivation of the Correct Treatment of 1/(eta.k)^p Singularities in Axial Gauges

TL;DR

This paper investigates the proper handling of singularities in axial gauge boson propagators by relating them to Lorentz gauge results through BRS transformations, revealing a complex structure without spurious poles.

Contribution

It provides a method to derive the axial gauge propagator from Lorentz gauge results, clarifying the singularity structure and ensuring no spurious poles are present.

Findings

Axial propagator has no spurious poles.

Singularity structure is complex near η·k=0.

Method relates axial and Lorentz gauge propagators via BRS transformations.

Abstract

We use the earlier results on the correlations of axial gauge Green's functions and the Lorentz gauge Green's functions obtained via finite field-dependent BRS transformations to study the question of the correct treatment of 1/(eta\cdot k)^p- type singularities in the axial gauge boson propagator. We show how the known treatment of the 1/(k^2)^n-type singularity in the Lorentz-type gauges can be used to write down the axial propagator via field transformation. We examine the singularity structure of the latter and find that the axial propagator so constructed has $no$ spurious poles, but a complex structure near $\eta\cdot k=0$.