QED Effective Action at Finite Temperature: Two-Loop Dominance

TL;DR

This paper calculates the two-loop effective action of QED at finite temperature, revealing that thermal photon excitations dominate over one-loop effects at low temperatures and uncovering new thermal contributions to pair production.

Contribution

It provides the first detailed calculation of the two-loop effective action of QED at finite temperature in the low-temperature regime, highlighting the dominance of two-loop effects.

Findings

Two-loop contributions surpass one-loop effects at low T.

Thermally induced effects significantly influence photon propagation.

Discovery of a thermal contribution to pair production in electric fields.

Abstract

We calculate the two-loop effective action of QED for arbitrary constant electromagnetic fields at finite temperature T in the limit of T much smaller than the electron mass. It is shown that in this regime the two-loop contribution always exceeds the influence of the one-loop part due to the thermal excitation of the internal photon. As an application, we study light propagation and photon splitting in the presence of a magnetic background field at low temperature. We furthermore discover a thermally induced contribution to pair production in electric fields.