• DOI:10.1063/1.4940122
• Corpus ID: 43604763

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

@article{Sok2014ThePA,
  title={The positronium and the dipositronium in a Hartree-Fock approximation of quantum electrodynamics},
  author={J'er'emy Sok},
  journal={Journal of Mathematical Physics},
  year={2014},
  volume={57},
  pages={022304}
}

• J'er'emy Sok
• Published 7 July 2014
• Physics
• Journal of Mathematical Physics

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∈12+Z+, we prove the existence of a critical point of the energy functional made of 2j + 1 electrons and 2j + 1 positrons.