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

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.

References in corpus (3)

• Geometric methods for nonlinear many-body quantum systems
• A new approach to the modelling of local defects in crystals: the reduced Hartree-Fock case
• Ground State and Charge Renormalization in a Nonlinear Model of Relativistic Atoms