Related papers: Discrete Gravity Models and Loop Quantum Gravity: …
We investigate the interaction mechanism of pure quantum gravity in Regge discretization. We compute volume-volume and link-link correlation functions. In a preliminary analysis the forces turn out to be of Yukawa type, at least on our…
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…
Content: 1. Introduction 2. Regge calculus and dynamical triangulations Simplicial manifolds and piecewise linear spaces - dual complex and volume elements - curvature and Regge action - topological invariants - quantum Regge calculus -…
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…
Polymer quantum mechanics has been studied as a simplified picture that reflects some of the key properties of Loop Quantum Gravity; however, while the fate of relativistic symmetries in Loop Quantum Gravity is still not established, it is…
We develop a proposal for a theory of simplicial gravity with spinors as the fundamental configuration variables. The underlying action describes a mechanical system with finitely many degrees of freedom, the system has a Hamiltonian and…
In this article we review the foundations and the present status of loop quantum gravity. It is short and relatively non-technical, the emphasis is on the ideas, and the flavor of the techniques. In particular, we describe the kinematical…
Simplicial approximation and the ideas associated with the Regge calculus.provide a concrete way of implementing a sum over histories formulation ofquantum gravity. A four-dimensional simplicial geometry is made up of flat four-simplices…
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…
Loop quantum gravity has provided us with a canonical framework especially devised for background independent and diffeomorphism invariant gauge field theories. In this quantization the fundamental excitations are called spin network…
The purpose of this contribution is to give an introduction to quantum geometry and loop quantum gravity for a wide audience of both physicists and mathematicians. From a physical point of view the emphasis will be on conceptual issues…
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…
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…
The most common spin foam models of gravity are widely believed to be discrete path integral quantizations of the Plebanski action. However, their derivation in present formulations is incomplete and lower dimensional simplex amplitudes are…
The study of toy models in loop quantum gravity (LQG), defined as truncations of the full theory, is relevant to both the development of the LQG phenomenology, in cosmology and astrophysics, and the progress towards the resolution of the…
I argue that the prediction of physical discreteness at the Planck scale in loop gravity is a reasonable conclusion that derives from a sensible ensemble of hypotheses, in spite of some contrary arguments considered in an interesting recent…
Loop quantum gravity, a non-perturbative and manifestly background free, quantum theory of gravity implies that at the kinematical level the spatial geometry is discrete in a specific sense. The spirit of background independence also…
Following recent developments in discrete gravity, we study geometrical variables (angles and forms) of simplices in the discrete geometry point of view. Some of our relatively new results include: new ways of writing a set of simplices…
Spin foam models of quantum gravity are based on Plebanski's formulation of general relativity as a constrained BF theory. We give an alternative formulation of gravity as BF theory plus a certain potential term for the B-field. When the…
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…