Existence of a stable polarized vacuum in the Bogoliubov-Dirac-Fock approximation
Abstract
According to Dirac's ideas, the vacuum consists of infinitely many virtual electrons which completely fill up the negative part of the spectrum of the free Dirac operator . In the presence of an external field, these virtual particles react and the vacuum becomes polarized. In this paper, following Chaix and Iracane ({\it J. Phys. B}, 22, 3791--3814, 1989), we consider the Bogoliubov-Dirac-Fock model, which is derived from no-photon QED. The corresponding BDF-energy takes the polarization of the vacuum into account and is bounded from below. A BDF-stable vacuum is defined to be a minimizer of this energy. If it exists, such a minimizer is solution of a self-consistent equation. We show the existence of a unique minimizer of the BDF-energy in the presence of an external electrostatic field, by means of a fixed-point approach. This minimizer is interpreted as the polarized vacuum.
Keywords
Cite
@article{arxiv.math-ph/0403005,
title = {Existence of a stable polarized vacuum in the Bogoliubov-Dirac-Fock approximation},
author = {Christian Hainzl and Mathieu Lewin and Eric Sere},
journal= {arXiv preprint arXiv:math-ph/0403005},
year = {2009}
}
Comments
final version, to appear in Commun. Math. Phys