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Letters in Mathematical Physics

, Volume 38, Issue 2, pp 217–220 | Cite as

Bound-state solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac systems

  • Maria J. Esteban
  • Vladimir Georgiev
  • Eric Séré
Article

Abstract

In this Letter we present a result concerning the existence of stationary solutions for the classical Maxwell-Dirac equations in the Lorentz gauge. We believe that such a result can be of interest for a field quantization approach in QED. This result is obtained by using variational arguments. By a similar method, we also find an infinity of distinct solutions for the Klein-Gordon-Dirac system, arising in the so-called Yukawa model.

Mathematics Subject Classifications (1991)

81T70 83A05 

Key words

Maxwell-Dirac equations Klein-Gordon-Dirac system Yukawa model stationary solutions field quantization 

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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Maria J. Esteban
    • 1
  • Vladimir Georgiev
    • 2
  • Eric Séré
    • 3
  1. 1.CEREMADE (URA CNRS 749)Université Paris DauphineParis Cedex 16France
  2. 2.Inst. of Math.Bulgarian Academy of SciencesSofiaBulgaria
  3. 3.Courant InstituteNew YorkU.S.A.

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