Behavior of the thermal gluon self-energy in the Coulomb gauge

TL;DR

This paper investigates the one-loop gluon self-energy in Coulomb gauge at finite temperature, confirming divergence cancellations and analyzing high-temperature behavior, revealing transverse and nonlocal leading terms and local sub-leading corrections.

Contribution

It provides a detailed analysis of gluon self-energy in Coulomb gauge at finite temperature, including divergence cancellation and high-temperature asymptotics, extending previous covariant gauge results.

Findings

Cancellation of energy divergences in the two-point function

Leading T^2 term is transverse and nonlocal at high temperature

Sub-leading ln(T) term is local and matches zero-temperature ultraviolet behavior

Abstract

We study, to one loop order, the behavior of the gluon self-energy in the non covariant Coulomb gauge at finite temperature. The cancellation of the peculiar energy divergences, which arise in such a gauge, is explicitly verified in the complete two point function of the Yang-Mills theory. At high temperatures, the leading T^2 term is determined to be transverse and nonlocal, in agreement with the results obtained in covariant gauges. The coefficient of the sub-leading ln(T) contribution, is non transverse but local and coincides (up to a multiplicative constant) with that of the ultraviolet pole term of the zero temperature amplitude.