Noncovariant gauges at zero and nonzero temperature

TL;DR

This paper reviews the challenges of using noncovariant gauges, especially the temporal axial gauge, in gauge-field perturbation theory at zero and finite temperatures, highlighting unresolved issues and partial solutions.

Contribution

It provides a critical review of the formalism for gauge-field perturbation theory in noncovariant gauges, emphasizing unresolved complications at zero and finite temperatures.

Findings

Complications exist in formulating gauge-field perturbation theory in noncovariant gauges.

Current solutions at finite temperature are limited to lowest order in coupling.

Uncertainty remains whether a fully consistent formalism exists for all calculations.

Abstract

I review the formalism for gauge-field perturbation theory in noncovariant gauges, particularly the temporal axial gauge. I show that, even at zero temperature, there are complications and it is not known whether a formalism exists for handling these that is correct for all calculations. For thermal field theory in the imaginary time formalism, there are different difficulties, whose solution so far is known only up to lowest order in the coupling $g$.