Nonrelativistic limit of Klein-Gordon-Maxwell to Schrodinger-Poisson
Analysis of PDEs
2007-05-23 v1
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.
Cite
@article{arxiv.math/0202201,
title = {Nonrelativistic limit of Klein-Gordon-Maxwell to Schrodinger-Poisson},
author = {Philippe Bechouche and Norbert Mauser and Sigmund Selberg},
journal= {arXiv preprint arXiv:math/0202201},
year = {2007}
}