Nonrelativistic limit of Klein-Gordon-Maxwell to Schrodinger-Poisson
Philippe Bechouche, Norbert Mauser, Sigmund Selberg
Abstract
We prove that in the nonrelativistic limit, solutions of the Klein-Gordon-Maxwell system in 1+3 dimensions converge in the energy space to solutions of a Schrodinger-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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