Statistics of spinning particles in 2+1 gravity

We examine the dynamics of $N$ spinning particles in 2+1 gravity, and obtain an effective Lagrangian description for the particles by eliminating the dreibeins and spin connections from the theory. The resulting equations of motion show that locally the particles are free, but globally their conserved momenta and angular momenta are not well defined. Conditions are found under which the effective action is invariant under particle exchanges. Ambiguities exist in passing to the quantum theory and these ambiguities can be exploited to obtain exotic statistics for the particles. We construct exchange operators which give exotic statistics, but which do not in general satisfy the braid group relations when $N>\mathrm{}2\mathrm{}$.