The pressure of QED from the two-loop 2PI effective action

TL;DR

This paper calculates the pressure of hot QED using a two-loop 2PI effective action, analyzing gauge dependence and suggesting Landau gauge minimizes gauge-related uncertainties.

Contribution

It provides the first two-loop 2PI calculation of QED pressure, highlighting gauge dependence and numerical stability considerations.

Findings

Gauge dependence is controlled for gauge parameter xi<1.

Landau gauge may reduce gauge-dependent effects.

Uncertainty due to gauge choice is manageable within certain parameters.

Abstract

We compute the pressure of hot quantum electrodynamics from the two-loop truncation of the 2PI effective action. Since the 2PI resummation guarantees gauge-fixing independence only up to the order of the truncation, our result for the pressure presents a gauge dependent contribution of O(e^4). We numerically characterize the credibility of this gauge-dependent calculation and find that the uncertainty due to gauge parameter dependence is under control for xi<1. Our calculation also suggests that the choice of Landau gauge may minimize gauge-dependent effects.