TY - JOUR

T1 - The positronium and the dipositronium in a Hartree-Fock approximation of quantum electrodynamics

AU - Sok, Jérémy Vithya

PY - 2016/2/1

Y1 - 2016/2/1

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.

U2 - 10.1063/1.4940122

DO - 10.1063/1.4940122

M3 - Journal article

AN - SCOPUS:84957989739

VL - 57

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 2

M1 - 022304

ER -