Related papers: A Ponzano-Regge model of Lorentzian 3-Dimensional …
The definition of the Ponzano-Regge state-sum model of three-dimensional quantum gravity with a class of local observables is developed. The main definition of the Ponzano-Regge model in this paper is determined by its reformulation in…
We show that the partition function of the Ponzano-Regge quantum gravity model can be written as a sum over surfaces in a $(2+1)$ dimensional space-time. We suggest a geometrical meaning, in terms of surfaces, for the (regulated)…
The Ponzano-Regge model of three-dimensional quantum gravity is well-defined when the observables satisfy a certain condition involving the twisted cohomology. In this case, the partition function is defined in terms of the Reidemeister…
The model of Lorentzian three-dimensional dynamical triangulations provides a non-perturbative definition of three-dimensional quantum gravity. The theory has two phases: a weak-coupling phase with quantum fluctuations around a…
It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat $SU(2)$ connections over a…
This article presents a derivation of the Ponzano--Regge model from a one-dimensional spinor action. The construction starts from the first-order Palatini formalism in three dimensions. We then introduce a simplicial decomposition of the…
Three-dimensional gravity is a topological field theory, which can be quantized as the Ponzano-Regge state-sum model built from the $\{3nj\}$-symbols of the recoupling of the $\SU(2)$ representations, in which spins are interpreted as…
We consider the path-sum of Ponzano-Regge with additional boundary contributions in the context of the holographic principle of Quantum Gravity. We calculate an holographic projection in which the bulk partition function goes to a…
We show that the normalized Lorentzian state sum is finite on any triangulation. It thus provides a candidate for a perturbatively finite quantum theory of general relativity in four dimensions with Lorentzian signature.
This is the first of a series of papers dedicated to the study of the partition function of three-dimensional quantum gravity on the twisted solid torus with the aim to deepen our understanding of holographic dualities from a…
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…
Three-dimensional Lorentzian quantum gravity, expressed as the continuum limit of a nonperturbative sum over spacetimes, is tantalizingly close to being amenable to analytical methods, and some of its properties have been described in terms…
The model which generalizes Ponzano and Regge $3D$ and Carfora-Martellini-Marzuoli $4D$ euclidean quantum gravity is considered. The euclidean Einstein-Regge action for a $D$-simplex is given in the semiclassical limit by a gaussian…
We study the semi-classical limit of the recently proposed coherent spin foam model for (2+1) Lorentzian quantum gravity. Specifically, we analyze the gluing equations derived from the stationary phase approximation of the vertex amplitude.…
We show how the expectation values of geometrical quantities in 3d quantum gravity can be explicitly computed using grasping rules. We compute the volume of a labelled tetrahedron using the triple grasping. We show that the large spin…
We present the construction of a new state sum model for $4d$ Lorentzian quantum gravity based on the description of quantum simplicial geometry in terms of edge vectors. Quantum states and amplitudes for simplicial geometry are built from…
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…
A well-defined regularized path integral for Lorentzian quantum gravity in three and four dimensions is constructed, given in terms of a sum over dynamically triangulated causal space-times. Each Lorentzian geometry and its associated…
Lorentzian quantum gravity is believed to cure the pathologies encountered in Euclidean quantum gravity, such as the conformal factor problem. We show that this is the case for the Lorentzian Regge path integral expanded around a flat…
The gauge gravity action for general relativity in any dimension using a connection for the Euclidean or Poincar\'e group and a symmetry-breaking scalar field is written using a particularly simple matrix technique. A discrete version of…