Canonical quantization of general relativity in discrete space-times.
Rodolfo Gambini,Jorge Pullin +1 more
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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.read more
Citations
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Background independent quantum gravity: A Status report
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Spin foam models for quantum gravity
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Flipped spinfoam vertex and loop gravity
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The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity
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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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Abhay Ashtekar,Abhay Ashtekar +1 more
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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.
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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.
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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.
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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.