Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of a stable polarized vacuum in the Bogoliubov-Dirac-Fock
  approximation   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, 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.

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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg