- 04-63 Christian HAINZL, Mathieu LEWIN and Eric SERE
- Existence of a stable polarized vacuum in the Bogoliubov-Dirac-Fock approximation
Mar 5, 04
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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 $D^0$. In the presence of an external field, these virtual particles react and the vacuum becomes polarized.
In this paper, following Chaix and Iracane, we consider the Bogoliubov-Dirac-Fock model, which is derived from 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 a solution of a self-consistent equation.
We show the existence of a 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.