Related papers: Fields and Laplacians on Quantum Geometries
We extend discrete calculus for arbitrary ($p$-form) fields on embedded lattices to abstract discrete geometries based on combinatorial complexes. We then provide a general definition of discrete Laplacian using both the primal cellular…
An approach to the discrete quantum gravity based on the Regge calculus is discussed which was developed in a number of our papers. Regge calculus is general relativity for the subclass of general Riemannian manifolds called piecewise flat…
We review the relation between Loop Quantum Gravity on a fixed graph and discrete models of gravity. We compare Regge and twisted geometries, and discuss discrete actions based on twisted geometries and on the discretization of the…
In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing…
We give a very concise review of the group field theory formalism for non-perturbative quantum gravity, a higher dimensional generalisation of matrix models. We motivate it as a simplicial and local realisation of the idea of 3rd…
Quantum geometry on a discrete set means a directed graph with a weight associated to each arrow defining the quantum metric. However, these `lattice spacing' weights do not have to be independent of the direction of the arrow. We use this…
This is a review of the results on black hole physics in the framework of loop quantum gravity. The key feature underlying the results is the discreteness of geometric quantities at the Planck scale predicted by this approach to quantum…
A model for quantum gravity in one (time) dimension is discussed, based on Regge's discrete formulation of gravity. The nature of exact continuous lattice diffeomorphisms and the implications for a regularized gravitational measure are…
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…
An algebraic formulation of Riemannian geometry on quantum spaces is presented, where Riemannian metric, distance, Laplacian, connection, and curvature have their counterparts. This description is also extended to complex manifolds.…
Simplicial approaches to quantum gravity such as Quantum Regge Calculus and Spin Foams include configurations where bulk edges can become arbitrarily large while keeping the lengths of the boundary edges small. Such configurations pose…
The review paper "Discrete Structures in Physics", written in 2000, describes how Regge's discretization of Einstein's theory has been applied in classical relativity and quantum gravity. Here, developments since 2000 are reviewed briefly,…
This is an informal review of the formulation of canonical general relativity and of its implications for quantum gravity; the various versions are compared, both in the continuum and in a discretized approximation suggested by Regge…
This is an introduction to the group field theory approach to quantum gravity, with emphasis on motivations and basic formalism, more than on recent results; we elaborate on the various ingredients, both conceptual and formal, of the…
The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial quantum theory proceeds via a discretization of…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at "quantum…
Euclidean quantum-gravity path-integrals are investigated within Regge calculus by computer simulations. The domain of integration is restricted by introducing a lower limit for the fatness of each simplex. We use the standard hypercubic…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
We give a short overview of the effective action approach in quantum field theory and quantum gravity and describe various methods for calculation of the asymptotic expansion of the heat kernel for second-order elliptic partial differential…