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Nonrelativistic limit of Klein-Gordon-Maxwell to Schrodinger-Poisson

Philippe Bechouche·Norbert Mauser·Sigmund Selberg
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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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Philippe Bechouche, Norbert Mauser, Sigmund Selberg. 2002-02-20. Nonrelativistic limit of Klein-Gordon-Maxwell to Schrodinger-Poisson. https://arxiv.org/abs/math/0202201

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