The Pauli-Villars-regularized Dirac vacuum in electromagnetic fields at positive temperature

TL;DR

This paper models the Dirac vacuum in electromagnetic fields at positive temperature using Pauli-Villars regularization to analyze vacuum polarization effects with electrostatic and magnetic potentials.

Contribution

It extends previous magnetic-only models by incorporating both electrostatic and magnetic fields in a finite-temperature Dirac vacuum using Pauli-Villars regularization.

Findings

Properly defines the free energy of the vacuum at positive temperature.

Provides a framework for studying polarization effects in the vacuum.

Extends prior magnetic-only models to include electrostatic potentials.

Abstract

In this paper we consider a model of the Dirac vacuum in classical electromagnetic fields at positive temperature. We adopt the Pauli-Villars regularisation technique in order to properly define the free energy of the vacuum, extending the previous work by the second named author on the purely magnetic case. This work is intended as a first step in understanding polarisation effects in the vacuum at positive temperature, in presence of both electrostatic and magnetic potentials.