Gauge Independence of Limiting Cases of One-Loop Electron Dispersion Relation in High-Temperature QED

TL;DR

This paper demonstrates that in high-temperature QED, the one-loop electron dispersion relation becomes gauge independent at high momenta, and the effective mass remains unaffected by gauge choices and leading temperature dependence.

Contribution

It proves gauge independence of the electron dispersion relation in the high-momentum limit and shows the effective mass is unaffected by gauge parameters at one-loop order.

Findings

Dispersion relation is gauge independent for momenta much larger than eT.

Effective mass of order eT is not corrected by order e^2T terms.

Gauge dependence of the self-energy does not influence the effective mass at high momenta.

Abstract

Assuming high temperature and taking subleading temperature dependence into account, gauge dependence of one-loop electron dispersion relation is investigated in massless QED at zero chemical potential. The analysis is carried out using a general linear covariant gauge. The equation governing the gauge dependence of the dispersion relation is obtained and used to prove that the dispersion relation is gauge independent in the limiting case of momenta much larger than $eT$. It is also shown that the effective mass is not influenced by the leading temperature dependence of the gauge dependent part of the effective self-energy. As a result the effective mass, which is of order $eT$, does not receive a correction of order $e^2T$ from one loop, independent of the gauge parameter.