A normalized solitary wave solution of the Maxwell-Dirac equations |
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| Institution: | 1. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Brazil;2. Dipartimento di Matematica, Politecnico di Milano, Italy;1. Department of Mathematics, Texas A & M University, College Station, TX 77843-3368, USA;2. Department of Mathematics, University of North Carolina - Chapel Hill, Chapel Hill, NC 27599, USA;3. Department of Mathematics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada |
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| Abstract: | We prove the existence of a -normalized solitary wave solution for the Maxwell-Dirac equations in (3+1)-Minkowski space. In addition, for the Coulomb-Dirac model, describing fermions with attractive Coulomb interactions in the mean-field limit, we prove the existence of the (positive) energy minimizer. |
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| Keywords: | Maxwell-Dirac equations Solitary waves Variational methods |
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