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Existence of a stable polarized vacuum in the Bogoliubov-Dirac-Fock approximation

dc.contributor.authorSéré, Eric
HAL ID: 171149
dc.contributor.authorLewin, Mathieu
HAL ID: 1466
ORCID: 0000-0002-1755-0207
dc.contributor.authorHainzl, Christian
dc.date.accessioned2009-07-09T08:22:03Z
dc.date.available2009-07-09T08:22:03Z
dc.date.issued2005
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/1016
dc.language.isoenen
dc.subjectMathematical Physicsen
dc.subjectPhysicsen
dc.subject.ddc519en
dc.titleExistence of a stable polarized vacuum in the Bogoliubov-Dirac-Fock approximationen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenAccording 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.en
dc.relation.isversionofjnlnameCommunications in Mathematical Physics
dc.relation.isversionofjnlvol257en
dc.relation.isversionofjnlissue3
dc.relation.isversionofjnldate2005
dc.relation.isversionofjnlpages515-562en
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s00220-005-1343-4
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelProbabilités et Mathématiques appliquéesen


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