Thermal forward scattering amplitudes in temporal gauges

TL;DR

This paper calculates the gluon self-energy at high temperatures in temporal gauges using thermal forward scattering amplitudes, revealing the structure of leading and sub-leading contributions and confirming transversality.

Contribution

It introduces a method to compute gluon self-energy in temporal gauges at high temperatures, including leading and sub-leading terms, and confirms transversality at one-loop and higher orders.

Findings

Leading T^2 and ln(T) contributions identified

Logarithmic terms match ultraviolet poles at zero temperature

Thermal self-energy remains transverse at one-loop and beyond

Abstract

We employ the thermal forward scattering amplitudes technique in order to compute the gluon self-energy in a class of temporal gauges. The leading T^2 and the sub-leading ln(T) contributions are obtained for temperatures high compared with the external momentum. The logarithmic contributions have the same structure as the ultraviolet pole terms which occur at zero temperature (we have recently extended this result to the Coulomb gauge). We also show that the prescription poles, characteristic of temporal gauges, do not modify the leading and sub-leading high-temperature behavior. The one-loop calculation shows that the thermal self-energy is transverse. This result has also been extended to higher orders, using the BRS identities.