The positronium in a mean-field approximation of quantum electrodynamics

TL;DR

This paper proves the existence of positronium, a bound state of an electron and a positron, within the Bogoliubov-Dirac-Fock mean-field model of quantum electrodynamics, highlighting a relativistic quantum bound state.

Contribution

It demonstrates the existence of positronium as a critical point of the energy functional in the BDF model without external fields, specifically modeling ortho-positronium.

Findings

Positronium exists as a bound state in the BDF model.

The state corresponds to a critical point of the energy functional.

The model describes ortho-positronium with parallel spins.

Abstract

The Bogoliubov-Dirac-Fock (BDF) model is a no-photon, mean-field approxi- mation of quantum electrodynamics. It describes relativistic electrons in the Dirac sea. In this model, a state is fully characterized by its one-body density matrix, an infinite rank nonnegative operator. We prove the existence of the positronium, the bound state of an electron and a positron, represented by a critical point of the energy functional in the absence of external field. This state is interpreted as the ortho-positronium, where the two particles have parallel spins.