Related papers: Testing the imposition of the Spin Foam Simplicity…
We propose a quantum version of the quadratic volume simplicity constraint for the EPRL spin foam model. It relies on a formula for the volume of 4-dimensional polyhedra, depending on its bivectors and the knotting class of its boundary…
A key point in the spin foam approach to quantum gravity is the implementation of simplicity constraints in the partition functions of the models. Here, we discuss the imposition of these constraints in a phase space setting corresponding…
We propose a new method of unifying gravity and the Standard Model by introducing a spin-foam model. We realize a unification between an SU(2) Yang-Mills interaction and 3D general relativity by considering a Spin(4) Plebanski action. The…
A classical foundation for an idea of reality condition in the context of spin foams (Barrett-Crane models) is developed. I extract classical real general relativity (all signatures) from complex general relativity by imposing the area…
In the first-order formulation, general relativity could be formally viewed as the topological $BF$ theory with a specific constraint, the Plebanski constraint. $BF$ theory is expected to be the classical limit of the Crane-Yetter~(CY)…
In this article we review the present status of the spin foam formulation of non-perturbative (background independent) quantum gravity. The article is divided in two parts. In the first part we present a general introduction to the main…
In the tetrad formulation of gravity, the so-called simplicity constraints play a central role. They appear in the Hamiltonian analysis of the theory, and in the Lagrangian path integral when constructing the gravity partition function from…
Spin foam models are an approach to quantum gravity based on the concept of sum over states, which aims to describe quantum spacetime dynamics in a way that its parent framework, loop quantum gravity, has not as of yet succeeded. Since…
Spin foam models for gravity or BF theory can be constructed by path integral formulation of the classical discrete models formulated on simplicial manifolds. Using this, we discuss the rigorous construction of Lorentzian spin foam models…
The simplicity constraint is studied in the context of 4d spinfoam models with cosmological constant. We find that the quantum simplicity constraint is realized as the 2d surface defect in SL(2,$\mathbb{C}$) Chern-Simons theory in the…
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 present a new $BF$-type action for complex general relativity with or without a cosmological constant resembling Plebanski's action, which depends on an SO(3,$\mathbb{C}$) connection, a set of 2-forms, a symmetric matrix, and a 4-form.…
We derive the the Barrett-Crane spin foam model for Euclidean 4 dimensional quantum gravity from a discretized BF theory, imposing the constraints that reduce it to gravity at the quantum level. We obtain in this way a precise prescription…
We perform, in a manifestly $SO(n-1,1)$ [$SO(n)$] covariant fashion, the Hamiltonian analysis of general relativity in $n$ dimensions written as a constrained $BF$ theory. We solve the constraint on the $B$ field in a way naturally adapted…
We report on the numerical analysis of the area correlations in spin foam gravity on a single 4-simplex considered by Rovelli in PRL 97 (2006) 151301. We compare the asymptotics and confirm the inverse squared distance leading behaviour at…
In this paper, we are going to discuss several approaches to solve the quadratic and linear simplicity constraints in the context of the canonical formulations of higher dimensional General Relativity and Supergravity developed in our…
It is well known that, in the first-order formalism, pure three-dimensional gravity is just the BF theory. Similarly, four-dimensional general relativity can be formulated as BF theory with an additional constraint term added to the…
Spin foams arise from a quantization of classical gravity expressed via the Plebanski action. Key open questions related to the continuum limit of spin foams are whether general relativity is reproduced and what type of corrections could…
The Barrett-Crane model for the SO(4,C) general relativity is systematically derived. This procedure makes rigorous the calculation of the Barrett-Crane intertwiners from the Barrett-Crane constraints of both real and complex Riemannian…
A dual formulation of group field theories, obtained by a Fourier transform mapping functions on a group to functions on its Lie algebra, has been proposed recently. In the case of the Ooguri model for SO(4) BF theory, the variables of the…