Ponzano–Regge model revisited: I. Gauge fixing, observables and interacting spinning particles

@article{Freidel2004PonzanoReggeMR,
  title={Ponzano–Regge model revisited: I. Gauge fixing, observables and interacting spinning particles},
  author={Laurent Freidel and David Louapre},
  journal={Classical and Quantum Gravity},
  year={2004},
  volume={21},
  pages={5685 - 5726}
}
We show how to properly gauge fix all the symmetries of the Ponzano–Regge model for 3D quantum gravity. This amounts to doing explicit finite computations for transition amplitudes. We give the construction of the transition amplitudes in the presence of interacting quantum spinning particles. We introduce a notion of operators whose expectation value gives rise to either gauge fixing, introduction of time, or insertion of particles, according to the choice. We give the link between the spin… 
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