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

F. A. Bais·N. M. Muller·B. J. Schroers
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Abstract

Starting with the Chern-Simons formulation of (2+1)-dimensional gravity we show that the gravitational interactions deform the Poincare symmetry of flat space-time 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.

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F. A. Bais, N. M. Muller, B. J. Schroers. 2002-05-02. Quantum group symmetry and particle scattering in (2+1)-dimensional quantum gravity. https://doi.org/10.1016/s0550-3213(02)00572-2

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