The positronium in a mean-field approximation of quantum electrodynamics.

Jérémy Sok (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

The Bogoliubov-Dirac-Fock (BDF) model is a no-photon, mean-field approxi- mation of quantum electrodynamics. It describes relativistic electrons in the Dirac sea. In this model, a state is fully characterized by its one-body density matrix, an infinite rank nonnegative operator. We prove the existence of the positronium, the bound state of an electron and a positron, represented by a critical point of the energy functional in the absence of external field. This state is interpreted as the ortho-positronium, where the two particles have parallel spins.

Mots clés: mean-field; positronium; Dirac operator; BDF energy; critical point

Domaines: Physique mathématique [math-ph]

Jérémy Sok. The positronium in a mean-field approximation of quantum electrodynamics.. 2014. ⟨hal-00991429⟩