
Existence of a stable polarized vacuum in the Bogoliubov-Dirac-Fock approximation
Séré, Eric; Lewin, Mathieu; Hainzl, Christian (2005), Existence of a stable polarized vacuum in the Bogoliubov-Dirac-Fock approximation, Communications in Mathematical Physics, 257, 3, p. 515-562. http://dx.doi.org/10.1007/s00220-005-1343-4
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Article accepté pour publication ou publiéDate
2005Nom de la revue
Communications in Mathematical PhysicsVolume
257Numéro
3Éditeur
Springer
Pages
515-562
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According to Diracrsquos 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 (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 the 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.Mots-clés
Mathematical Physics; PhysicsPublications associées
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Hainzl, Christian; Lewin, Mathieu; Séré, Eric (2009) Article accepté pour publication ou publié
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Séré, Eric; Lewin, Mathieu; Hainzl, Christian; Gravejat, Philippe (2012) Communication / Conférence
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Séré, Eric; Hainzl, Christian; Lewin, Mathieu (2005) Article accepté pour publication ou publié
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Solovej, Jan Philip; Séré, Eric; Lewin, Mathieu; Hainzl, Christian (2007-06) Article accepté pour publication ou publié