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

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(e4)O(e4). We numerically characterize the credibility of this gauge-dependent calculation and find that the uncertainty due to gauge parameter dependence is under control for ξ≲1ξ≲1. Our calculation also suggests that the choice of Landau gauge may minimize gauge-dependent effects.