| dc.contributor.author | Séré, Eric | |
| dc.contributor.author | Hainzl, Christian | |
| dc.contributor.author | Lewin, Mathieu | |
| dc.date.accessioned | 2009-07-03T12:53:03Z | |
| dc.date.available | 2009-07-03T12:53:03Z | |
| dc.date.issued | 2005 | |
| dc.identifier.uri | https://basepub.dauphine.fr/handle/123456789/731 | |
| dc.language.iso | en | en |
| dc.subject | Mathematical Physics | en |
| dc.subject.ddc | 520 | en |
| dc.title | Self-consistent solution for the polarized vacuum in a no-photon QED model | en |
| dc.type | Article accepté pour publication ou publié | |
| dc.description.abstracten | We study the Bogoliubov–Dirac–Fock model introduced by Chaix and Iracane (1989 J. Phys. B: At. Mol. Opt. Phys. 22 3791–814) which is a mean-field theory deduced from no-photon QED. The associated functional is bounded from below. In the presence of an external field, a minimizer, if it exists, is interpreted as the polarized vacuum and it solves a self-consistent equation. In a recent paper, we proved the convergence of the iterative fixed-point scheme naturally associated with this equation to a global minimizer of the BDF functional, under some restrictive conditions on the external potential, the ultraviolet cut-off Λ and the bare fine structure constant α. In the present work, we improve this result by showing the existence of the minimizer by a variational method, for any cut-off Λ and without any constraint on the external field. We also study the behaviour of the minimizer as Λ goes to infinity and show that the theory is 'nullified' in that limit, as predicted first by Landau: the vacuum totally cancels the external potential. Therefore, the limit case of an infinite cut-off makes no sense both from a physical and mathematical point of view. Finally, we perform a charge and density renormalization scheme applying simultaneously to all orders of the fine structure constant α, on a simplified model where the exchange term is neglected. | en |
| dc.relation.isversionofjnlname | Journal of Physics A: Mathematical and General | |
| dc.relation.isversionofjnlvol | 38 | en |
| dc.relation.isversionofjnlissue | 20 | en |
| dc.relation.isversionofjnldate | 2005 | |
| dc.relation.isversionofjnlpages | 4483-4499 | en |
| dc.relation.isversionofdoi | http://dx.doi.org/10.1088/0305-4470/38/20/014 | en |
| dc.description.sponsorshipprivate | oui | en |
| dc.relation.isversionofjnlpublisher | IOP Publishing | en |
| dc.subject.ddclabel | Sciences connexes (physique, astrophysique) | en |
