Cahiers du CEREMADE 

Unité
Mixte de Recherche du C.N.R.S. N°7534 

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 $D0$. 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 BogoliubovDiracFock model, which is derived from QED. The corresponding BDFenergy takes the polarization of the vacuum into account and is bounded from below. A BDFstable vacuum is defined to be a minimizer of this energy. If it exists, such a minimizer is a solution of a selfconsistent equation.
We show the existence of a minimizer of the BDFenergy in the presence of an external electrostatic field, by means of a fixedpoint approach. This minimizer is interpreted as the polarized vacuum. 





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