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Open AccessJournal ArticleDOI

Canonical quantization of general relativity in discrete space-times.

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TLDR
This work analyzes discrete lattice general relativity and develops a canonical formalism that allows one to treat constrained theories in Lorentzian signature space-times in a manner that makes the quantization of the theories conceptually clear, albeit computationally involved.
Abstract
It has long been recognized that lattice gauge theory formulations, when applied to general relativity, conflict with the invariance of the theory under diffeomorphisms. We analyze discrete lattice general relativity and develop a canonical formalism that allows one to treat constrained theories in Lorentzian signature space-times. The presence of the lattice introduces a "dynamical gauge" fixing that makes the quantization of the theories conceptually clear, albeit computationally involved. The problem of a consistent algebra of constraints is automatically solved in our approach. The approach works successfully in other field theories as well, including topological theories. A simple cosmological application exhibits quantum elimination of the singularity at the big bang.

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Citations
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Background independent quantum gravity: A Status report

TL;DR: Loop quantum gravity as discussed by the authors is a background-independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of geometry.
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Spin foam models for quantum gravity

TL;DR: In this paper, the authors present a review of spin foam formulations of nonperturbative (background-independent) quantum gravity and define the Barrett-Crane model for four-dimensional gravity.
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Flipped spinfoam vertex and loop gravity

TL;DR: In this article, a vertex amplitude for 4d loop quantum gravity was derived from a conventional quantization of a Regge discretization of euclidean general relativity, which yields a spinfoam sum that corrects some difficulties of the Barrett-Crane theory.
Journal ArticleDOI

The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity

TL;DR: In this paper, the authors proposed a solution to this set of problems based on the so-called master constraint which combines the smeared Hamiltonian constraints for all smearing functions into a single constraint.
Journal ArticleDOI

Fundamental structure of loop quantum gravity

TL;DR: In this article, the fundamental structure of loop quantum gravity is presented pedagogically and a semi-classical analysis is carried out to test the classical limit of the quantum theory.
References
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Journal ArticleDOI

New variables for classical and quantum gravity.

TL;DR: A Hamiltonian formulation of general relativity based on certain spinorial variables is introduced that enables one to imbed the constraint surface in the phase space of Einstein's theory into that of Yang-Mills theory.
Journal ArticleDOI

Real Ashtekar variables for Lorentzian signature space-times.

J F G Barbero
- 15 May 1995 - 
TL;DR: In this paper, a modified Hamiltonian constraint in the usual $SO(3)$ Yang-Mills phase space was proposed to describe space-times with Lorentzian signature without the introduction of complex variables.
Journal ArticleDOI

Quantum Spin Dynamics (QSD)

TL;DR: In this article, an anomaly-free spin-network operator corresponding to the Wheeler-DeWitt constraint of Lorentzian, four-dimensional, canonical, non-perturbative vacuum gravity is constructed in the continuum.
Journal ArticleDOI

Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action

TL;DR: Barbero’s Hamiltonian formulation is derived from an action, which can be considered as a generalization of the ordinary Hilbert-Palatini action, and provides a real theory of gravity with a connection as configuration variable, and with the usual Gauss and vector constraint.
Book ChapterDOI

An Introduction to spin foam models of quantum gravity and BF theory

TL;DR: In this article, a self-contained introduction to spin foam models of quantum gravity and a simpler field theory called BF theory is provided. But it is not a complete overview of spin networks.