Charge renormalization and static electron/positron pair production for a nonlinear Dirac model with weak interactions (Q2855122)

The Bogoliubov-Dirac-Fock (BDF) model gives a description of relativistic electrons in external fields that accounts both for the infinitely many virtual electrons of Dirac's vacuum and the Coulomb interactions between all the particles. This paper studies static electron/positron pair production in the BDF model. When interactions are present in the system, the state of the system is an infinite-rank projection satisfying a nonlinear equation. In particular, the author gives solutions to the nonlinear equation under weak interactions and strong external fields. The result is used to find the critical strength of the external potential required to produce an additional particle in the vacuum and conclude that, due to charge renormalization, static pair production occurs in the interacting case under a stronger field than in the noninteracting case.