The positronium and the dipositronium in a Hartree-Fock approximation of quantum electrodynamics

The Bogoliubov-Dirac-Fock (BDF) model is a no-photon approximation of quantum electrodynamics. It allows to study relativistic electrons in interaction with the Dirac sea. A state is fully characterized by its one-body density matrix, an infinite rank nonnegative projector. We prove the existence of...

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Bibliographic Details
Published in:arXiv.org 2014-09
Main Author: Sok, Jérémy
Format: Article
Language:English
Subjects:
Critical point
Electrons
Hartree approximation
Mathematical analysis
Positronium
Positrons
Quantum electrodynamics
Quantum theory
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Summary:The Bogoliubov-Dirac-Fock (BDF) model is a no-photon approximation of quantum electrodynamics. It allows to study relativistic electrons in interaction with the Dirac sea. A state is fully characterized by its one-body density matrix, an infinite rank nonnegative projector. We prove the existence of the para-positronium, the bound state of an electron and a positron with antiparallel spins, in the BDF model represented by a critical point of the energy functional in the absence of external field. We also prove the existence of the dipositronium, a molecule made of two electrons and two positrons that also appears as a critical point. More generally, for any half integer \(j\in \tfrac{1}{2}+\mathbb{Z}_+\), we prove the existence of a critical point of the energy functional made of \(2j+1\) electrons and \(2j+1\) positrons.
ISSN:2331-8422