Path Integral Approach to Residual Gauge Fixing

TL;DR

This paper investigates residual gauge fixing in path integrals for axial-type and light-cone gauges, revealing different structures and dependencies in the propagator formulations due to residual symmetries.

Contribution

It provides a detailed analysis of residual gauge fixing in axial-type and light-cone gauges, highlighting their distinct impacts on propagator structures and prescription dependence.

Findings

Residual gauge fixing fully determines propagators in axial-type gauges.

Light-cone gauge exhibits prescription dependence due to global symmetry.

Different residual gauge fixing structures affect propagator formulations.

Abstract

In this paper we study the question of residual gauge fixing in the path integral approach for a general class of axial-type gauges including the light-cone gauge. We show that the two cases -- axial-type gauges and the light-cone gauge -- lead to very different structures for the explicit forms of the propagator. In the case of the axial-type gauges, fixing the residual symmetry determines the propagator of the theory completely. On the other hand, in the light-cone gauge there is still a prescription dependence even after fixing the residual gauge symmetry, which is related to the existence of an underlying global symmetry.