Canonical quantization and braid invariance of (2 + 1)-dimensional gravity coupled to point particles

We investigate the canonical quantization of gravity coupled to pointlike matter in 2 + 1 dimensions, starting from the usual point particle action, and working in the first order formalism. By introducing an auxiliary variable, we make the theory locally Poincaré invariant. The enlarged symmetry group simplifies the analysis of diffeomorphism invariance. In the passage to the quantum theory, a nontrivial cocycle is found. This is responsible for braid invariance analogous to that found in non-Abelian Chern-Simons and conformal field theories, and is responsible for the nontrivial gravitational scattering. Finally the relation to the theories introduced by 't Hooft and Carlip is explained.