Starting with the Chern–Simons formulation of (2+1)-dimensional gravity we show that the gravitational interactions deform the Poincaré 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.
- 2+1 DIMENSIONAL GRAVITY
- 2-PARTICLE SCATTERING
- CLASSICAL SCATTERING
Bais, F. A., Muller, N. M., & Schroers, B. J. (2002). Quantum group symmetry and particle scattering in (2+1)-dimensional quantum gravity. Nuclear Physics B, 640(1-2), 3-45. https://doi.org/10.1016/S0550-3213(02)00572-2