Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-05-03
Int.J.Mod.Phys. A13 (1998) 5503-5518
Physics
High Energy Physics
High Energy Physics - Theory
21 pages, Latex, 3 figures included
Scientific paper
10.1142/S0217751X9800250X
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 ${\cal M}=SU(1,1)/U(1)$. 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.
Kim Sung-Soo
Oh Phillial
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