NONRELATIVISTIC LIMIT OF CHERN-SIMONS GAUGED FIELD EQUATIONS

Abstract

We study the nonrelativistic limit of the Chern-Simons-Dirac system on R1+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 c corresponding to the initial data for the Dirac spinor psi(c)(0) which is bounded in H-s for 1/2 < s < 1. Next we show that if the initial data psi(c)(0) 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 Schrodinger equation in C ([0, T]; H-s') for s' < s.