Flat Connections on Quantum Bundles and Fractional Statistic in Geometric Quantization

摘要

It is shown that in the geometric quantization formulation fractional statistics in a quantized system of N indistinguishable particles in two spatial dimensions arise from the nontrivial cohomology of the flat connection on the quantum line bundle as well as from the nontrival homology of the configuration space. The propagator of an nonrelativistic interacting system with fractional statistics is derived.