The positronium and the dipositronium in a HartreeFock approximation of quantum electrodynamics
Abstract
The BogoliubovDiracFock (BDF) model is a nophoton approximation of quantum electrodynamics. It allows to study relativistic electrons in interaction with the Dirac sea. A state is fully characterized by its onebody density matrix, an infinite rank nonnegative projector. We prove the existence of the parapositronium, 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 $j\in \tfrac{1}{2}+\mathbb{Z}_+$, we prove the existence of a critical point of the energy functional made of $2j+1$ electrons and $2j+1$ positrons.
 Publication:

arXiv eprints
 Pub Date:
 July 2014
 arXiv:
 arXiv:1407.1602
 Bibcode:
 2014arXiv1407.1602S
 Keywords:

 Mathematical Physics
 EPrint:
 arXiv admin note: text overlap with arXiv:1405.3928