Related papers: Path integral representation of spin foam models o…

In this article we give a systematic definition of the recently introduced spin foam models for four dimensional quantum gravity reviewing the main results on their semiclassical limit on fixed discretizations.

We show that the Euclidean and Lorentzian EPRL vertex amplitudes of covariant Loop Quantum Gravity are related through a ``Wick rotation'' of the real Immirzi parameter to purely imaginary values. Our result follows from the simultaneous…

We study the generalised constrained BF theory described in gr-qc/0102073 in order to introduce the Immirzi parameter in spin foam models. We show that the resulting spin foam model is still based on simple representations and that the…

The fusion coefficients from SO(3) to SO(4) play a key role in the definition of spin foam models for the dynamics in Loop Quantum Gravity. In this paper we give a simple analytic formula of the EPRL fusion coefficients. We study the large…

This is a review paper about one of the approaches to unify Quantum Mechanics and the theory of General Relativity. Starting from the pioneer work of Regge and Penrose other scientists have constructed state sum models, as Feymann path…

The 1-parameter family of transformations identified by Barbero and Immirzi plays a significant role in non-perturbative approaches to quantum gravity, among them Loop Quantum Gravity and Spin Foams. It facilitates the loop quantization…

We study the state-sum models of quantum gravity based on a representation 2-category of the Poincare 2-group. We call them spin-cube models, since they are categorical generalizations of spin-foam models. A spin-cube state sum can be…

We study the semiclassical behavior of Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam model, by taking into account of the sum over spins in the large spin regime. The large spin parameter \lambda and small Barbero-Immirzi…

In this note we study the correspondence between the ``relativistic spin foam'' model introduced by Barrett, Crane and Baez and the so(4) Plebanski action. We argue that the $so(4)$ Plebanski model is the continuum analog of the…

Spin foam models are the path integral counterparts to loop quantized canonical theories. In the last few years several spin foam models of gravity have been proposed, most of which live on finite simplicial lattice spacetime. The lattice…

In the quest of a physical theory of quantum gravity, spin foam models, or in short spinfoams, propose a well-defined path integral summing over quantized discrete space-time geometries. At the crossroad of topological quantum field theory,…

The goal of this paper is to introduce a systematic approach to spin foams. We define operator spin foams, that is foams labelled by group representations and operators, as the main tool. An equivalence relation we impose in the set of the…

Starting from the reformulation of the classical phase space of Loop Quantum Gravity in terms of spinor variables and spinor networks, we build coherent spin network states and show how to use them to write the spinfoam path integral for…

A number of approaches to four-dimensional quantum gravity, such as loop quantum gravity and holography, situate areas as their fundamental variables. However, this choice of kinematics can easily lead to gravitational dynamics peaked on…

Dimerized quantum spin systems may appear under several circumstances, e.g\ by a modulation of the antiferromagnetic exchange coupling in space, or in frustrated quantum antiferromagnets. In general, such systems display a quantum phase…

We revise imposition of various constraints in spin foam models of 4-dimensional general relativity. We argue that the usual simplicity constraint must be supplemented by a constraint on holonomies and together they must be inserted…

We show that the degenerate sector of Spin(4) Plebanski formulation of four-dimensional gravity is exactly solvable and describes covariantly embedded SU(2) BF theory. This fact ensures that its spin foam quantization is given by the SU(2)…

This article reviews the present status of the spin foam approach to the quantization of gravity. Special attention is payed to the pedagogical presentation of the recently introduced new models for four dimensional quantum gravity. The…

We develop a path integral representation for the dynamics of quantum systems with a finite-dimensional Hilbert space, formulated entirely within a discrete phase space. Starting from the discrete Wigner function defined on $\mathbb{Z}_d…

The amplitude for the 4-simplex in a spin foam model for quantum gravity is defined using a graphical calculus for the unitary representations of the Lorentz group. The asymptotics of this amplitude are studied in the limit when the…