The positronium and the dipositronium in a Hartree-Fock approximation of quantum electrodynamics.
Sok, Jérémy (2014), The positronium and the dipositronium in a Hartree-Fock approximation of quantum electrodynamics.. https://basepub.dauphine.fr/handle/123456789/13745
TypeDocument de travail / Working paper
External document linkhttp://hal.archives-ouvertes.fr/hal-01018933
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Abstract (EN)The Bogoliubov-Dirac-Fock (BDF) model is a no-photon approximation of quan- tum 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 elec- trons and two positrons that also appears as a critical point. More generally, for any half integer j ∈ 1 +Z+, we prove the existence of a critical point of the energy 2 functional made of 2j + 1 electrons and 2j + 1 positrons.
Subjects / Keywordspositronium; Borwein and Preiss Lemma; mountain pass; Hilbert manifold; Dirac sea
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