't HOOFT'S SCATTERING AMPLITUDE FROM CHERN–SIMONS–WITTEN GRAVITY IN 2+1 DIMENSIONS

By using canonical phase space variables different from those associated with individual particles, we couple the Chern–Simons–Witten gravity to point-like sources. The resulting theory provides an alternative to the usual test particle approximation and yields 't Hooft's scattering amplitude in the limit of two very massive slowly moving particles.