Relativistic Quantum Theory with Fractional Spin and Statistics

TL;DR

This paper explores the formulation of relativistic quantum mechanics with fractional spin and statistics in 2+1 dimensions, emphasizing path-integral methods and group-theoretical foundations.

Contribution

It provides a comprehensive path-integral approach to fractional spin and statistics in a relativistic setting, including the construction of multi-particle systems and discussion of related field theory issues.

Findings

Path-integral formulation of relativistic fractional spin systems

Analysis of spin-statistics relation in 2+1 dimensions

Resolution of field theory problems with fractional statistics

Abstract

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.