Quantum group symmetry and particle scattering in (2+1)-dimensional quantum gravity

Starting with the Chern-Simons formulation of (2 + 1)-dimensional gravity we show that the gravitational interactions deform the Poincare symmetry of flat spacetime to a quantum group symmetry. The relevant quantum group is the quantum double of the universal cover of the (2 + 1) dimensional Lorentz group, or Lorentz double for short. We construct the Hilbert space of two gravitating particles and use the universal R-matrix of the Lorentz double to derive a general expression for the scattering cross section of gravitating particles with spin. In appropriate limits our formula reproduces the semi-classical scattering formulae found by 't Hooft, Deser, Jackiw and de Sousa Gerbert. (C) 2002 Elsevier Science B.V. All rights reserved.