Absence of binding in a mean-field approximation of quantum electrodynamics

Jérémy Sok (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We study the Bogoliubov-Dirac-Fock model which is a mean-field approximation of QED. It allows to consider relativistic electrons interacting with the Dirac sea. We study the system of two electrons in the vacuum: it has been shown in a previous work that an electron alone can bind due to the vacuum polarization, under some technical assumptions. Here we prove the absence of binding for the system of two electrons: the response of the vacuum is not sufficient to counterbalance the repulsion of the electrons.

Keywords: Dirac operator; Dirac sea; Pekar-Tomasevitch model; no binding

Domains: Mathematical Physics [math-ph]

Jérémy Sok. Absence of binding in a mean-field approximation of quantum electrodynamics. 2014. ⟨hal-01018932v1⟩