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

Jérémy Vithya Sok

doi:10.1063/1.4940122

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

Jérémy Vithya Sok^*

^*Corresponding author af dette arbejde

Institut for Matematiske Fag

1 Citationer (Scopus)

Abstract

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 non-negative 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 an 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 ∈ 1/2 + Z₊, we prove the existence of a critical point of the energy functional made of 2j + 1 electrons and 2j + 1 positrons.

Originalsprog	Engelsk
Artikelnummer	022304
Tidsskrift	Journal of Mathematical Physics
Vol/bind	57
Udgave nummer	2
Antal sider	37
ISSN	0022-2488
DOI	https://doi.org/10.1063/1.4940122
Status	Udgivet - 1 feb. 2016

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10.1063/1.4940122

Citationsformater

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N2 - 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 non-negative 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 an 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 ∈ 1/2 + Z+, we prove the existence of a critical point of the energy functional made of 2j + 1 electrons and 2j + 1 positrons.

AB - 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 non-negative 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 an 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 ∈ 1/2 + Z+, we prove the existence of a critical point of the energy functional made of 2j + 1 electrons and 2j + 1 positrons.

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DO - 10.1063/1.4940122

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ER -

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

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