2014/07/07 by Jérémy Sok, Sok, Jérémy
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1407.1602
arXiv admin note: text overlap with arXiv:1405.3928
openalex publication_date 2014/07/07 · arxiv created 2014/09/15 · arxiv updated 2014/09/16 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
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∈ \tfrac12+ℤ+, we prove the existence of a critical point of the energy functional made of 2j+1 electrons and 2j+1 positrons.