A reformulation of the Ponzano-Regge quantum gravity model in terms of surfaces

We reformulate the Ponzano-Regge quantum gravity model in terms of surfaces on a 3-dimensional simplex lattice. This formulation (1) has a clear relation to the loop representation of the canonical quantum general relativity in 3-dimensions, (2) may have a 4-dimensional analogue, in contrast to the 6-j symbolic formalism of the Ponzano-Regge model, and (3) is purely a theory of surfaces, in the sense that it does not include any field variables; hence it is coordinate-free on the surface and background-free in spacetime. We discuss implications and applications of this formulation.Comment: latex 11 page

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

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)Comment: 48 pages, 15 figure

Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory

We study the no gravity limit G_{N}-> 0 of the Ponzano-Regge amplitudes with massive particles and show that we recover in this limit Feynman graph amplitudes (with Hadamard propagator) expressed as an abelian spin foam model. We show how the G_{N} expansion of the Ponzano-Regge amplitudes can be resummed. This leads to the conclusion that the dynamics of quantum particles coupled to quantum 3d gravity can be expressed in terms of an effective new non commutative field theory which respects the principles of doubly special relativity. We discuss the construction of Lorentzian spin foam models including Feynman propagatorsComment: 46 pages, the wrong file was first submitte

Holonomy observables in Ponzano-Regge type state sum models

We study observables on group elements in the Ponzano-Regge model. We show that these observables have a natural interpretation in terms of Feynman diagrams on a sphere and contrast them to the well studied observables on the spin labels. We elucidate this interpretation by showing how they arise from the no-gravity limit of the Turaev-Viro model and Chern-Simons theory.Comment: 15 pages, 2 figure

12j-symbols and four-dimensional quantum gravity

We propose a model which represents a four-dimensional version of Ponzano and Regge's three-dimensional euclidean quantum gravity. In particular we show that the exponential of the euclidean Einstein-Regge action for a $4d$-discretized block is given, in the semiclassical limit, by a gaussian integral of a suitable $12j$-symbol. Possible developments of this result are discussed.Comment: 12 pages, Late