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Phys. Rev. A 76, 052104 (2007) [11 pages]

Minimization method for relativistic electrons in a mean-field approximation of quantum electrodynamics

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Christian Hainzl*
University of Alabama, Birmingham, Alabama 35294, USA

Mathieu Lewin†
CNRS and Université de Cergy-Pontoise, Laboratoire “AGM” UMR8088, 2 Avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France

Eric Séré‡
Université Paris Dauphine, CEREMADE UMR7534, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France

Jan Philip Solovej§
Department of Mathematics, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark

Received 11 June 2007; published 7 November 2007

We study a mean-field relativistic model which is able to describe both the behavior of finitely many spin-1∕2 particles such as electrons and of the Dirac sea which is self-consistently polarized in the presence of the real particles. The model is derived from the QED Hamiltonian in Coulomb gauge neglecting the photon field. All our results are nonperturbative and mathematically rigorous.

© 2007 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevA.76.052104
DOI:
10.1103/PhysRevA.76.052104
PACS:
12.20.−m, 31.15.−p

*hainzl@math.uab.edu

†Mathieu.Lewin@math.cnrs.fr

‡sere@ceremade.dauphine.fr

§solovej@math.ku.dk

 
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