Finite temperature gluon self-energy in a class of temporal gauges

TL;DR

This paper calculates the gluon self-energy at finite temperature in a class of temporal gauges, showing it remains transverse and deriving leading thermal contributions, with results matching zero-temperature ultraviolet structures.

Contribution

It demonstrates that gluon self-energy in temporal gauges is exactly transverse at finite temperature, unlike covariant gauges, and provides explicit high-temperature expansions.

Findings

Gluon self-energy is transverse at finite temperature in the studied gauges.

Leading T^2 and ln(T) contributions are derived for high temperatures.

Logarithmic terms mirror zero-temperature ultraviolet divergences.

Abstract

The approach which relates thermal Green functions to forward scattering amplitudes of on-shell thermal particles is applied to the calculation of the gluon self-energy, in a class of temporal gauges. We show to all orders that, unlike the case of covariant gauges, the exact self-energy of the gluon is transverse at finite temperature. The leading T^2 and the sub-leading ln(T) contributions are obtained for temperatures T high compared with the external momentum. The logarithmic contributions have the same structure as the ultraviolet pole terms which occur at zero temperature.