A Minimization Method for Relativistic Electrons in a Mean-Field Approximation of Quantum Electrodynamics

TL;DR

This paper introduces a rigorous, non-perturbative mean-field relativistic model for electrons and the Dirac sea derived from QED, enabling analysis of their self-consistent polarization without photon interactions.

Contribution

It develops a mathematically rigorous, non-perturbative mean-field model for relativistic electrons and the Dirac sea based on the QED Hamiltonian, neglecting photons.

Findings

Model captures behavior of electrons and Dirac sea

Provides a rigorous mathematical framework

Enables analysis of self-consistent polarization

Abstract

We study a mean-field relativistic model which is able to describe both the behavior of finitely many spin-1/2 particles like electrons and of the Dirac sea which is self-consistently polarized in the presence of the real particles. The model is derived from the QED Hamiltonian in Coulomb gauge neglecting the photon field. All our results are non-perturbative and mathematically rigorous.