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NONRELATIVISTIC LIMIT OF CHERN-SIMONS GAUGED FIELD EQUATIONS

  • Chae, Myeongju (Department of Applied Mathematic Hankyong National University) ;
  • Yim, Jihyun (Department of Mathematics Chung-Ang University University)
  • Received : 2017.07.12
  • Accepted : 2017.11.02
  • Published : 2018.07.31

Abstract

We study the nonrelativistic limit of the Chern-Simons-Dirac system on ${\mathbb{R}}^{1+2}$. As the light speed c goes to infinity, we first prove that there exists an uniform existence interval [0, T] for the family of solutions ${\psi}^c$ corresponding to the initial data for the Dirac spinor ${\psi}_0^c$ which is bounded in $H^s$ for ${\frac{1}{2}}$ < s < 1. Next we show that if the initial data ${\psi}_0^c$ converges to a spinor with one of upper or lower component zero in $H^s$, then the Dirac spinor field converges, modulo a phase correction, to a solution of a linear $Schr{\ddot{o}}dinger$ equation in C([0, T]; $H^{s^{\prime}}$) for s' < s.

Keywords

Chern-Simons-Dirac system;nonrelativistic limit

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