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

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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.

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Authors and Affiliations

  1. CEREMADE (URA CNRS 749), Université Paris Dauphine, 75775, Paris Cedex 16, France

    Maria J. Esteban

  2. Inst. of Math., Bulgarian Academy of Sciences, Acad. G. Bonchev Str. bl. 8, 1113, Sofia, Bulgaria

    Vladimir Georgiev

  3. Courant Institute, 251 Mercer Street, 10003, New York, NY, U.S.A.

    Eric Séré

Authors
  1. Maria J. Esteban
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  2. Vladimir Georgiev
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  3. Eric Séré
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Additional information

Supported by contract MM-31 with Bulgarian Ministry of Culture, Science and Education and A. Von Humboldt Foundation.

Partially supported by NSF grant DMS-9114456.

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Esteban, M.J., Georgiev, V. & Séré, E. Bound-state solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac systems. Lett Math Phys 38, 217–220 (1996). https://doi.org/10.1007/BF00398323

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  • DOI: https://doi.org/10.1007/BF00398323

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