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

Details Ponzano-Regge model revisited I: Gauge fixing, observables and interacting spinning particles Ponzano-Regge model revisited I: Gauge fixing, observables and interacting spinning particles

2004-01-12

arxiv.org/abs/hep-th/0401076v1

Class.Quant.Grav. 21 (2004) 5685-5726

Physics

High Energy Physics

High Energy Physics - Theory

48 pages, 15 figures

Scientific paper

10.1088/0264-9381/21/24/002

We show how to properly gauge fix all the symmetries of the Ponzano-Regge model for 3D quantum gravity. This amounts to do 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 foam quantization and the hamiltonian quantization. We finally show the link between Ponzano-Regge model and the quantization of Chern-Simons theory based on the double quantum group of SU(2)

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