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 for this work

Department of Mathematical Sciences

1 Citation (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.

Original language	English
Article number	022304
Journal	Journal of Mathematical Physics
Volume	57
Issue number	2
Number of pages	37
ISSN	0022-2488
DOIs	https://doi.org/10.1063/1.4940122
Publication status	Published - 1 Feb 2016

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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.",

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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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JF - Journal of Mathematical Physics

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

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