Geodesic
Two Hartree-Fock models for the vacuum polarization
[Deux modèles de Hartree-Fock pour la polarisation du vide]
Gravejat, Philippe1  ; Hainzl, Christian2  ; Lewin, Mathieu3  ; Séré, Éric4 
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.

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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.

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.

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
Mots-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

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 
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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://geodesic.mathdoc.fr/articles/10.5802/jedp.87/

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