A Nonlinear Model for Relativistic Electrons at Positive Temperature

TL;DR

This paper develops a non-perturbative relativistic electron model at positive temperature within the Hartree-Fock framework, analyzing minimizers with and without exchange terms, extending prior zero-temperature results.

Contribution

It introduces a self-consistent, non-perturbative approach for relativistic electrons at positive temperature, including existence and properties of minimizers.

Findings

Existence of minimizers in the relativistic electron-positron field.

Extension of zero-temperature results to positive temperature.

Analysis of the impact of exchange terms on the model.

Abstract

We study the relativistic electron-positron field at positive temperature in the Hartree-Fock-approximation. We consider both the case with and without exchange term, and investigate the existence and properties of minimizers. Our approach is non-perturbative in the sense that the relevant electron subspace is determined in a self-consistent way. The present work is an extension of previous work by Hainzl, Lewin, S\'er\'e, and Solovej where the case of zero temperature was considered.