 04398 Christian HAINZL, Mathieu LEWIN, Eric SERE
 Existence of a stable polarized vacuum in the BogoliubovDiracFock approximation
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Nov 26, 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 ({\it J. Phys. B}, 22,
37913814, 1989), we consider the BogoliubovDiracFock model, which
is derived from nophoton 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 solution of a selfconsistent equation.
We show the existence of a unique 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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