Related papers: On the volume simplicity constraint in the EPRL sp…
We derive simplicity constraints for the quantization of general Lorentzian 4-geometries. Our method is based on the correspondence between coherent states and classical bivectors and the minimization of associated uncertainties. For…
In this article we consider specific bivector geometries which arise in the large-spin limit of the extension of the Engle-Pereira-Rovelli-Livine spin foam model for quantum gravity by Kaminski, Kisielowski and Lewandowski. We address the…
In this article we consider non-convex $4d$ polytopes in $\mathbb{R}^4$. The paper consist of two parts: Firstly, we extend the proof of the formula for the $4d$ volume in terms of $2d$ face bivectors and boundary graph crossings from…
Spin Foam and Loop approaches to Quantum Gravity reformulate Einstein's theory of relativity in terms of connection variables. The metric properties are encoded in face bivectors/conjugate fluxes that are required to satisfy certain…
We study the asymptotic properties of four-simplex amplitudes for various four-dimensional spin foam models. We investigate the semi-classical limit of the Ooguri, Euclidean and Lorentzian EPRL models using coherent states for the boundary…
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…
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…
The semiclassical limit of a 4-simplex amplitude for a spin foam quantum gravity model with an Immirzi parameter is studied. If the boundary state represents a non-degenerate 4-simplex geometry, the asymptotic formula contains the Regge…
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…
We introduce a three-dimensional Plebanski action for the gauge group SO(4). In this model, the $B$ field satisfies quadratic simplicity constraints similar to that of the four-dimensional Plebanski theory, but with the difference that the…
We revise the classical continuum formulation behind the Spin Foam approach to the quantization of gravity. Based on the recent applications of the current EPRL-FK model beyond triangulations, we identify the tension with the implementation…
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…
Spin foam models, an approach to defining the dynamics of loop quantum gravity, make use of the Plebanski formulation of gravity, in which gravity is recovered from a topological field theory via certain constraints called simplicity…
We investigate a way of imposing simplicity constraints in a holomorphic Spin Foam model that we recently introduced. Rather than imposing the constraints on the boundary spin network, as is usually done, one can impose the constraints…
The spectral dimension has proven to be a very informative observable to understand the properties of quantum geometries in approaches to quantum gravity. In loop quantum gravity and its spin foam description, it has not been possible so…
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…
A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In this paper we reconsider the implementation of the…
In this article, we consider an ad-hoc deformation of the EPRL model for quantum gravity by a cosmological constant term. This sort of deformation has been first introduced by Han for the case of the $4$-simplex. In this article, we…
We overview the volume calculations for polyhedra in Euclidean, spherical and hyperbolic spaces. We prove the Sforza formula for the volume of an arbitrary tetrahedron in $H^3$ and $S^3$. We also present some results, which provide a…
By use of H. C. Wang's bound on the radius of a ball embedded in the fundamental domain of a lattice of a semisimple Lie group, we construct an explicit lower bound for the volume of a quaternionic hyperbolic orbifold that depends only on…