Statistical Mechanics of Anyons

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1. First, three-body problem of anyons is studied. It has been known for sometime that semiclassical two-body partition function reproduces exact second virial coefficient. We tried to generalize this for three-anyon problem. By introducing a projective operator written in terms of hyperspherical coordinate, we could separate the trace into a subtrace over the space of irreducible representation of the symmetric group. This will be reported shortly.2. We also looked at many-anyon problem on topologically nontrivial surface. According to the braid group analysis, the statistical parameter is quantized on a cylinder. We studied this problem by requiring the uniqueness of the anyon wave function and found that the wave function is well defined for any value of the statistical parameter. We also studied an exact multi-anyon wave function. We are seeking for a possibility that with a certain interaction the exact wave function may be obtained.3, In the quantum field theory, an anyon is realized as a vortex in Chern-Simons gauge theory and it is quite important to investigate the structure of the vortices in general system. For this purpose, we have developed a technique to compute the free energy of a vortex-bearing system at an arbitrary temperature. We have applied this technique to a solution in polyacetylene and a vortex line in a type II superconductor as a preliminary. Application to Chern-Simons vortex is under progress.