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Archive for Rational Mechanics and Analysis

, Volume 208, Issue 2, pp 603–665 | Cite as

Construction of the Pauli–Villars-Regulated Dirac Vacuum in Electromagnetic Fields

  • Philippe Gravejat
  • Christian Hainzl
  • Mathieu Lewin
  • Éric Séré
Article

Abstract

Using the Pauli–Villars regularization and arguments from convex analysis, we construct solutions to the classical time-independent Maxwell equations in Dirac’s vacuum, in the presence of small external electromagnetic sources. The vacuum is not an empty space, but rather a quantum fluctuating medium which behaves as a nonlinear polarizable material. Its behavior is described by a Dirac equation involving infinitely many particles. The quantum corrections to the usual Maxwell equations are nonlinear and nonlocal. Even if photons are described by a purely classical electromagnetic field, the resulting vacuum polarization coincides to first order with that of full Quantum Electrodynamics.

Keywords

Electromagnetic Field Quantum Electrodynamic Fourth Order Term Lagrangian Action Resolvent Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Philippe Gravejat
    • 1
  • Christian Hainzl
    • 2
  • Mathieu Lewin
    • 3
  • Éric Séré
    • 4
  1. 1.Centre de Mathématiques Laurent Schwartz (UMR 7640)Palaiseau CedexFrance
  2. 2.Mathematisches InstitutTübingenGermany
  3. 3.CNRS & Laboratoire de Mathématiques (UMR 8088)Université de Cergy-PontoiseCergy-PontoiseFrance
  4. 4.Ceremade (UMR 7534), Université Paris-DauphinePlace du Maréchal de Lattre de TassignyParis Cedex 16France

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