SPIN AND STATISTICS OF GRAVITATIONAL ANYONS

We determine the spin and statistics of a particle in 2 + 1 dimensions coupled to linearized gravity with a Chern-Simons term. The model and the results are compared to those of the corresponding abelian vector theory. The statistics emerge from the effective particle-particle interaction, while the spin is computed using the symmetric stress tensor of the system. We find that the spin-statistics relation is satisfied. In the gravitational case we show that while stress tensors are never gauge invariant, the Poincaré generators are; in particular, despite subtleties peculiar to two spatial dimensions, there are no "superpotential" ambiguities in these generators. © 1990.