Two Hartree-Fock models for the vacuum polarization

Gravejat, Philippe; Hainzl, Christian; Lewin, Mathieu; Séré, Éric

doi:10.5802/jedp.87

Two Hartree-Fock models for the vacuum polarization
[Deux modèles de Hartree-Fock pour la polarisation du vide]

Gravejat, Philippe ¹ ; Hainzl, Christian ² ; Lewin, Mathieu ³ ; Séré, Éric ⁴

¹ Centre de Mathématiques Laurent Schwartz (UMR 7640) École Polytechnique F-91128 Palaiseau Cedex France
² Mathematisches Institut Auf der Morgenstelle 10 D-72076 Tübingen Germany
³ Centre National de la Recherche Scientifique and Laboratoire de Mathématiques (UMR 8088) Université de Cergy-Pontoise F-95000 Cergy-Pontoise France
⁴ Centre de Recherche en Mathématiques de la Décision (UMR 7534) Université Paris-Dauphine Place du Maréchal De Lattre de Tassigny F-75775 Paris Cedex 16 France

Journées équations aux dérivées partielles (2012), article no. 4, 31 p.

Résumé
Abstract

Nous présentons des résultats récents sur la dérivation et l’analyse de deux modèles de type Hartree-Fock pour la polarisation du vide. Nous portons une attention particulière à la construction variationnelle d’un vide polarisé auto-consistent, et à la pertinence physique de notre construction non perturbative vis-à-vis de la description perturbative donnée par l’électrodynamique quantique.

We review recent results about the derivation and the analysis of two Hartree-Fock-type models for the polarization of vacuum. We pay particular attention to the variational construction of a self-consistent polarized vacuum, and to the physical agreement between our non-perturbative construction and the perturbative description provided by Quantum Electrodynamics.

EuDML

DOI : 10.5802/jedp.87

Classification : 35Q41, 49S05, 81T16, 81V10
Keywords: Vacuum polarization, Dirac sea, Hartree-Fock approximation, Bogoliubov-Dirac-Fock model, Pauli-Villars regularization, charge renormalization, quantum electrodynamics
Mot clés : Polarisation du vide, mer de Dirac, approximation de type Hartree-Fock, modèle de Bogoliubov-Dirac-Fock, régularisation de Pauli-Villars, renormalisation de la charge, électrodynamique quantique

Affiliations des auteurs :

Gravejat, Philippe ¹ ; Hainzl, Christian ² ; Lewin, Mathieu ³ ; Séré, Éric ⁴

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Gravejat, Philippe; Hainzl, Christian; Lewin, Mathieu; Séré, Éric. Two Hartree-Fock models for the vacuum polarization. Journées équations aux dérivées partielles (2012), article  no. 4, 31 p. doi : 10.5802/jedp.87. http://www.numdam.org/articles/10.5802/jedp.87/

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