m at h . A P / 02 02 20 1 v 1 20 F eb 2 00 2 Nonrelativistic limit of Klein - Gordon - Maxwell to Schrödinger - Poisson Philippe
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چکیده
We prove that in the nonrelativistic limit c → ∞, where c is the speed of light, solutions of the Klein-Gordon-Maxwell system on R 1+3 converge in the energy space C([0, T ]; H 1) to solutions of a Schrödinger-Poisson system, under appropriate conditions on the initial data. This requires the splitting of the scalar Klein-Gordon field into a sum of two fields, corresponding, in the physical interpretation, to electrons and positrons.
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ar X iv : m at h / 02 02 20 1 v 1 [ m at h . A P ] 2 0 Fe b 20 02 Nonrelativistic limit of Klein - Gordon - Maxwell to Schrödinger - Poisson
We prove that in the nonrelativistic limit c → ∞, where c is the speed of light, solutions of the Klein-Gordon-Maxwell system on R 1+3 converge in the energy space C([0, T ]; H 1) to solutions of a Schrödinger-Poisson system, under appropriate conditions on the initial data. This requires the splitting of the scalar Klein-Gordon field into a sum of two fields, corresponding, in the physical int...
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We prove that in the nonrelativistic limit c → ∞, where c is the speed of light, solutions of the Klein-Gordon-Maxwell system on R1+3 converge in the energy space C([0, T]; H1) to solutions of a Schrödinger-Poisson system, under appropriate conditions on the initial data. This requires the splitting of the scalar Klein-Gordon field into a sum of two fields, corresponding, in the physical interp...
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