A rigorous justification of the Mittleman's approach to the Dirac--Fock model

TL;DR

This paper rigorously justifies the Dirac--Fock model as a valid variational approximation of quantum electrodynamics in certain regimes, and explores related properties of the model for atoms and molecules.

Contribution

It provides a rigorous mathematical foundation for the Dirac--Fock model as an approximation of QED when parameters are small or large, and introduces new properties of the model.

Findings

Justifies Dirac--Fock as a variational approximation of QED.

Proves no-unfilled shells property in certain regimes.

Establishes new properties of the Dirac--Fock model.

Abstract

In this paper, we study the relationship between the Dirac--Fock model and the electron-positron Hartree--Fock model. We justify the Dirac--Fock model as a variational approximation of QED when the vacuum polarization is neglected and when the fine structure constant $\alpha$ is small and the velocity of light $c$ is large. As a byproduct, we also prove, when $\alpha$ is small or $c$ is large, the no-unfilled shells theory in the Dirac--Fock theory for atoms and molecules. The proof is based on some new properties of the Dirac--Fock model.