  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.
