Abelian Chern-Simons field theory and anyon equation on a cylinder

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Abstract

We present the anyon equation on a cylinder and in an infinite potential wall from the abelian Chern-Simons theory coupled to non-relativistic matter field by obtaining the effective hamiltonian through the canonical transformation method used for the theory on a plane and on a torus. We also give the periodic property of the theory on the cylinder.

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Classical and quantal nonrelativistic Chern-Simons theory

R. Jackiw, So-Young Pi (1990)

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Schr\"{o}dinger Fields on the Plane with \([U(1)]^N\) Chern-Simons Interactions and Generalized Self-dual Solitons

Pyungwon Ko, Hyunsoo Min, Bum-Hoon Lee … (1993)

A general non-relativistic field theory on the plane with couplings to an arbitrary number of abelian Chern-Simons gauge fields is considered. Elementary excitations of the system are shown to exhibit fractional and mutual statistics. We identify the self-dual systems for which certain classical and quantal aspects of the theory can be studied in a much simplified mathematical setting. Then, specializing to the general self-dual system with two Chern-Simons gauge fields (and non-vanishing mutual statistics parameter), we present a systematic analysis for the static vortexlike classical solutions, with or without uniform background magnetic field. Relativistic generalizations are also discussed briefly.