Nonperturbative QED Effective Action at Finite Temperature

TL;DR

This paper introduces a new method to calculate the finite-temperature effective action in QED for time-dependent electric fields, accounting for nonequilibrium pair production, vacuum polarization, and thermal effects.

Contribution

It presents a novel approach to derive the finite-temperature effective action for nonequilibrium quantum fields in QED, including explicit results for constant electric fields.

Findings

Finite-temperature effective action includes thermal loops and vacuum fluctuations.

Imaginary part relates to pair production, real part to vacuum polarization and thermal effects.

Explicit calculation of effective action in a constant electric field.

Abstract

We advance a novel method for the finite-temperature effective action for nonequilibrium quantum fields and find the QED effective action in time-dependent electric fields, where charged pairs evolve out of equilibrium. The imaginary part of the effective action consists of thermal loops of the Fermi-Dirac or Bose-Einstein distribution for the initial thermal ensemble weighted with factors for vacuum fluctuations. And the real part of the effective action is determined by the mean number of produced pairs, vacuum polarization, and thermal distribution. The mean number of produced pairs is equal to twice the imaginary part. We explicitly find the finite-temperature effective action in a constant electric field.