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

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

2002-05-02

arxiv.org/abs/hep-th/0205021v1

Nucl.Phys. B640 (2002) 3-45

Physics

High Energy Physics

High Energy Physics - Theory

45 pages, amslatex

Scientific paper

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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