RELATIVISTIC QUANTUM-FIELD THEORY WITH FRACTIONAL SPIN AND STATISTICS

We construct a relativistic quantum field theory in 2 + 1 dimensions whose Fock states provide a multivalued representation of the Poincare group. We add a topological term to the action of a scalar field theory and we show that this endows the path integral of the theory with an operator-valued cocycle which modifies the transformation properties of physical states. We demonstrate that one-particle states carry (in general) fractional spin. We determine the spin of many-particle states and we prove a generalized spin-statistics relation. We propose an equation of motion for on-shell states which generalizes naturally the Dirac equation.