Abstract
We develop the relativistic quantum mechanics of particles with fractional spin and statistics in 2 + 1 dimensions in the path-integral approach. We endow the elementary excitations of the theory with fractional spin through the coupling of the particle number current with a topological term. We work out the dynamics of the spin degrees of freedom, and display the relation between the spin action and the knot invariants of the paths contributing to the path integral. We show that the explicit spin-changing interaction can be traded for multivaluedness of the wave function, and we relate this to the representation theory of the Lorentz and Poincaré groups in 2 + 1 dimensions. We discuss the multiparticle dynamics and derive the spin–statistics theorem.
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