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

2002/02/20 by Philippe Bechouche, Bechouche, Philippe, Norbert J. Mauser +4 · 1 citation
Mathematics · #35Q40 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions #math.AP #msc:35Q40

paper · pdf · doi:10.48550/arxiv.math/0202201

arxiv created 2002/02/20 · openalex publication_date 2002/02/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Optimal convergence rates of the Klein-Gordon-Schrödinger system in the nonrelativistic limit

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