Stationary solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac equations |
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| Authors: | Maria J Esteban Vladimir Georgiev Eric Séré |
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| Institution: | (1) CEREMADE, URA CNRS 749, Université Paris Dauphine, Place de Lattre de Tassigny, F-75775 Paris Cedex 16, France;(2) Institute of Mathematics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. bl. 8, 1113 Sofia, Bulgaria;(3) Courant Institute of Mathematical Sciences, 251 Mercer Street, 10003 New York, NY, USA |
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| Abstract: | The Maxwell-Dirac system describes the interaction of an electron with its own electromagnetic field. We prove the existence of soliton-like solutions of Maxwell-Dirac in (3+1)-Minkowski space-time. The solutions obtained are regular, stationary in time, and localized in space. They are found by a variational method, as critical points of an energy functional. This functional is strongly indefinite and presents a lack of compactness. We also find soliton-like solutions for the Klein-Gordon-Dirac system, arising in the Yukawa model.Supported by Contract MM-31 with Bulgarian Ministry of Culture, Science and Education and Alexander Von Humboldt Foundation.Partially supported by NSF grant DMS-9114456. |
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| Keywords: | 49S05 81V10 35Q60 35Q51 |
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