NONPERTURBATIVE GAUGE THEORETIC TREATMENT OF 2-PARTICLE SCATTERING IN (2+1)-DIMENSIONAL GRAVITY

By a suitable choice of phase space variables, which is natural for the reduction of a two-body problem, we couple two sources to the Chern-Simons-Witten action and obtain the exact two-body Hamiltonian. For particles of (nearly) equal mass and of small momenta, the Hamiltonian reduces to that of 't Hooft. In the corresponding geometry, when viewed froin a particular frame, the relative coordinate moves on a cone of deficit angle equal to the classical Hamiltonian.