Application of finite field-dependent BRS transformations to problems of the Coulomb gauge

TL;DR

This paper uses finite field-dependent BRS transformations to analyze the Coulomb gauge in quantum field theory, revealing its features, limit behaviors, and reproducing known two-loop integral results without extra regularization.

Contribution

It introduces a method connecting Coulomb and Lorentz gauges via BRS transformations, clarifying gauge limit behaviors and reproducing complex two-loop results within the path integral framework.

Findings

Coulomb gauge must be treated as the limit lambda --> 0.

The propagator exhibits good high energy behavior for nonzero lambda and epsilon.

The method reproduces Cheng and Tsai's two-loop integral results without extra regularization.

Abstract

We discuss the Coulomb propagator in the formalism developed recently in which we construct the Coulomb gauge path-integral by correlating it with the well-defined Lorentz gauge path-integrals through a finite field-dependent BRS transformation. We discover several features of the Coulomb gauge from it. We find that the singular Coulomb gauge HAS to be treated as the gauge parameter lambda --> 0 limit. We further find that the propagator so obtained has good high energy behavior (k_0^{-2}) for lambda and epsilon nonzero. We further find that the behavior of the propagator so obtained is sensitive to the order of limits k_0 -->infinity, lambda -->0 and epsilon --> 0; so that these have to be handled carefully in a higher loop calculation. We show that we can arrive at the result of Cheng and Tsai for the ambiguous two loop Feynman integrals without the need for an extra ad hoc regularization and within the path integral formulation.