Absence of binding in a mean-field approximation of quantum electrodynamics

TL;DR

This paper investigates a mean-field model of quantum electrodynamics and proves that two electrons do not bind due to vacuum polarization effects, highlighting limitations of the model in capturing electron interactions.

Contribution

The study demonstrates the absence of binding in a two-electron system within a mean-field QED approximation, contrasting with previous results for a single electron.

Findings

Two electrons do not bind in the model.

Vacuum polarization does not overcome electron repulsion.

The model's limitations in describing multi-electron binding.

Abstract

We study the Bogoliubov-Dirac-Fock model which is a mean-field approximation of QED. It allows to consider relativistic electrons interacting with the Dirac sea. We study the system of two electrons in the vacuum: it has been shown in a previous work that an electron alone can bind due to the vacuum polarization, under some technical assumptions. Here we prove the absence of binding for the system of two electrons: the response of the vacuum is not sufficient to counterbalance the repulsion of the electrons.