BRST analysis of 2+1 gravity

The classical formulation and the canonical and path-integral quantization of triad Einstein gravity in 2+1 dimensions is discussed using the Hamiltonian Becchi-Rouet-Stora-Tyutin (BRST) approach. We construct the BRST charge and demonstrate explicitly the BRST symmetry of the theory. We show explicitly that for this particular system, where both approaches can be carried up to their last consequences, the canonical BRST quantization coincides exactly with Dirac quantization. We also show how to construct from the BRST-invariant action the gauge-fixed action used by Witten to calculate topology-changing amplitudes.