Nonrelativistic limit of Chern-Simons gauged field equations
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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 12 <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\"{o}dinger equation in $C([0, T]; H^{s'})$ for $ s' <s $.
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 12 <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\"{o}dinger equation in $C([0, T]; H^{s'})$ for $ s' <s $.
참고문헌 (12)
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