Related papers: From spin foams to area metric dynamics to gravito…

A number of approaches to 4D quantum gravity, such as holography and loop quantum gravity, propose areas instead of lengths as fundamental variables. The Area Regge action, which can be defined for general 4D triangulations, is a natural…

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…

Spin foam models for quantum gravity are derived from lattice path integrals. The setting involves variables from both lattice BF theory and Regge calculus. The action consists in a Regge action, which depends on areas, dihedral angles and…

Discretization of general relativity is a promising route towards quantum gravity. Discrete geometries have a finite number of degrees of freedom and can mimic aspects of quantum geometry. However, selection of the correct discrete freedoms…

Spin foam vertex amplitudes are the key ingredient of spin foam models for quantum gravity. These fall into the realm of discretized path integral, and can be seen as generalized lattice gauge theories. They can be seen as an attempt at a…

The asymptotics of some spin foam amplitudes for a quantum 4-simplex is known to display rapid oscillations whose frequency is the Regge action. In this note, we reformulate this result through a difference equation, asymptotically…

The Regge Calculus is a powerful method to approximate a continuous manifold by a simplicial lattice, keeping the connectivities of the underlying lattice fixed and taking the edge lengths as degrees of freedom. The Discrete Regge Model…

Any approach to pure quantum gravity must eventually face the question of coupling quantum matter to the theory. In the past, several ways of coupling matter to spin foam quantum gravity have been proposed, but the dynamics of the coupled…

The first computation of a spin foam dynamics that provides a test of the quantum equations of motions of gravity is presented. Specifically, a triangulation that includes an inner edge is treated. The computation leverages the recently…

We define an effective action for spin foam models of quantum gravity by adapting the background field method from quantum field theory. We show that the Regge action is the leading term in the semi-classical expansion of the spin foam…

We introduce the basic elements of SO(n)-local theory of Regge Calculus. A first order formalism, in the sense of Palatini, is defined on the metric-dual Voronoi complex of a simplicial complex. The Quantum Measure exhibits an expansion, in…

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…

While the use of spin networks has greatly improved our understanding of the kinematical aspects of quantum gravity, the dynamical aspects remain obscure. To address this problem, we define the concept of a `spin foam' going from one spin…

A lattice quantum gravity model in 4 dimensional Riemannian spacetime is constructed based on the SU(2) Ashtekar formulation of general relativity. This model can be understood as one of the family of models sometimes called ``spin foam…

We propose a regularized lattice model for quantum gravity purely formulated in terms of fermions. The lattice action exhibits local Lorentz symmetry, and the continuum limit is invariant under general coordinate transformations. The metric…

Lattice spinor gravity is a proposal for regularized quantum gravity based on fermionic degrees of freedom. In our lattice model the local Lorentz symmetry is generalized to complex transformation parameters. The difference between space…

We consider Riemannian 4d BF lattice gauge theory, on a triangulation of spacetime. Introducing the simplicity constraints which turn BF theory into simplicial gravity, some geometric quantities of Regge calculus, areas, and 3d and 4d…

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…

We present a formulation of Regge Calculus where arbitrary coordinates are associated to each vertex of a simplicial complex and the degrees of freedom are given by the metric on each simplex. The lengths of the edges are thus determined…

Simplicial approaches to quantum gravity such as quantum Regge calculus and spin foams include configurations where bulk edges can become arbitrarily large while the boundary edges are kept small. Spikes and spines are prime examples for…