Relativistic Quantum Theory with Fractional Spin and Statistics

Details Relativistic Quantum Theory with Fractional Spin and Statistics Relativistic Quantum Theory with Fractional Spin and Statistics

1993-07-07

arxiv.org/abs/hep-th/9307047v1

Physics

High Energy Physics

High Energy Physics - Theory

77 pages, three figures (not included, available upon request from author), plain TeX with harvmac (b mode), DFTT-93-33

Scientific paper

These lectures discuss the formulation of quantum mechanics with fractional spin and statistics in 2+1 dimensions in a relativistic setting, emphasizing the path-integral approach. The non-relativistic theory is reviewed from a path-integral viewpoint. The group-theoretical underpinnings of relativistic fractional spin are discussed, then the path-integral quantization of spin and of massive fermions without using spinors is reviewed. The path integral for a system of n relativistic particles with fractional spin is constructed, the spin-statistics relation and the Lorentz and Poincare' representation content of physical states are discussed. Some problems in formulating a field theory with fractional statistics are presented, and their resolution in the operator cocycle approach is reviewed.

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