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On the Gauged Non-compact Spin System
We examine classical and quantum aspects of the planar non-compact spin
system coupled with Chern-Simons gauge field in the presence of background
charge. We first define our classical spin system as non- relativistic
non-linear sigma model in which the order parameter spin takes value in the
non-compact manifold . Although the naive model does not
allow any finite energy self dual solitons, it is shown that the gauged system
admits static Bogomol'nyi solitons with finite energy whose rotationally
symmetric soliton solutions are analyzed in detail. We also discuss the large
spin limit in which the self-dual equation reduces to the well-known gauged
non- linear Schr\"odinger model or Abelian Higgs model, depending on the choice
of the background charge term. Then, we perform quantization of the model. We
find that the spin algebra satisfies anomalous commutation relations, and the
system is a field theoretic realization of the anyons.Comment: 21 pages, Latex, 3 figures include