Laurent Freidel and David Louapre 2004 Class. Quantum Grav. 21 5685 doi:10.1088/0264-9381/21/24/002
Laurent Freidel1,2 and David Louapre2
Show affiliationsWe 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 foam quantization and the Hamiltonian quantization. We finally show the link between the Ponzano–Regge model and the quantization of Chern–Simons theory based on the double quantum group of SU(2).
83C27 Lattice gravity, Regge calculus and other discrete methods
81T70 Quantization in field theory; cohomological methods (See also 58D29)
81T13 Yang-Mills and other gauge theories (See also 53C07, 58E15)
Issue 24 (21 December 2004)
Received 22 January 2004, in final form 10 September 2004
Published 22 November 2004
Laurent Freidel and David Louapre 2004 Class. Quantum Grav. 21 5685
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