On the Hartree-Fock equations of the electron/positron field

TL;DR

This paper investigates the Hartree-Fock equations for relativistic electron-positron fields, proving the existence of minimizers and characterizing their properties within a quantum field theoretical framework.

Contribution

It establishes the existence of minimizers for the relativistic Hartree-Fock energy functional and shows they are purely electronic states satisfying no-pair Dirac-Fock equations.

Findings

Existence of a minimizer for the energy functional.

Minimizers are purely electronic states and projections.

Minimizers satisfy no-pair Dirac-Fock equations.

Abstract

We study the energy of relativistic electrons and positrons interacting via the second quantized Coulomb potential in the field of a nucleus of charge Z within the Hartree-Fock approximation. We show that the associated functional has a minimizer. In addition, all minimizers are purely electronic states, they are projections, and fulfill the no-pair Dirac-Fock equations.