ON SPIN AND (QUANTUM) GRAVITY IN 2 + 1 DIMENSIONS

We analyze the interaction of point particles in a gauge theory for gravity in 2 + 1 dimensions with particular emphasis on the effects of spin. It is shown that the known space-time solution for spinning sources in Einstein gravity exhibits torsion at the location of the sources. In the gauge theory of gravity, spin arises naturally as one of the charges of the Poincaré group and is not quantized for minkowskian (as opposed to euclidean) signature. Although the full action still looks topological, this property is spoiled by the identification of the coordinates of the particles with "internal" variables of the Poincaré group. We demonstrate the calculation of gravitational scattering amplitudes as an Aharonov-Bohm effect for a particle minimally coupled to the Poincaré field. The interpretation of the dreibein as a soldering form is abandoned and the results of Einstein's theory are recovered from the gauge theory without constructing a metric. © 1990.