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

By L. Freidel, David Louapre. 2004

240 citations recorded by the source corpus.

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 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).

Subfields: Applied Mathematics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/00cdf95514e4588876a724fec6ede5123e2d724b

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In Applied Mathematics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

The Complete 1/N Expansion of Colored Tensor Models in Arbitrary Dimension (2011, methodology): “In the most common GFT models [7,8] the Feynman amplitude of a graph equals the partition function of BF theory [ 19 ,20] discretized on the dual gluing of simplices.”
Loop Quantum Gravity (2003, background): “In the spin-foam formalism, an interesting line of investigation has studied the coupling of particles in 3D, treated as topological defects [118, 119, 209, 117, 116, 220, 108].”
The Spin-Foam Approach to Quantum Gravity (2012, background): “In the spin-foam literature, this has been considered form the canonical perspective in [279, 280] and from the covariant perspective extensively by Freidel and Louapre [188].”
The 1/N Expansion of Colored Tensor Models (2010, methodology): “For the simplest GFT models [15], the Feynman amplitude of a graph equals the partition function of the discretized BF theory [ 16 ,17].”
Introduction to doubly special relativity (2004, background): “In the standard Special Relativity we have only one scale, and there is no natural way in which another scale of mass and/or length could be introduced purely in Special Relativistic setting.”