SCHRODINGER FIELDS ON THE PLANE WITH [U(1)](N) CHERN-SIMONS INTERACTIONS AND GENERALIZED SELF-DUAL SOLITONS

A general nonrelativistic 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 ce rtain classical and quantal aspects of the theory can be studied in a much simplified mathematical setting. Then, specializing to the genera l self-dual system with two Chern-Simons gauge fields (and nonvanishin g mutual statistics parameter), we present a systematic analysis for t he static vortexlike classical solutions, with or without a uniform ba ckground magnetic field. Relativistic generalizations are also discuss ed briefly.