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A Finiteness proof for the Lorentzian state sum spin foam model for quantum general relativity
TLDR
In this article, it was shown that the normalized Lorentzian state sum is finite on any triangulation, and thus provides a candidate for a perturbatively finite quantum theory of general relativity in four dimensions with Lorentziian signature.Abstract:
We show that the normalized Lorentzian state sum is finite on any triangulation. It thus provides a candidate for a perturbatively finite quantum theory of general relativity in four dimensions with Lorentzian signature.read more
Citations
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LQG vertex with finite Immirzi parameter
TL;DR: In this article, the authors extend the definition of the flipped loop-quantum gravity vertex to the case of a finite Immirzi parameter γ, and show that the resulting dynamics is defined on a Hilbert space isomorphic to the one of loop quantum gravity.
Journal ArticleDOI
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.
LQG vertex with finite Immirzi parameter
TL;DR: In this article, the authors extend the definition of the flipped loop-quantum-gravity vertex to the case of a finite Immirzi parameter, and show that the resulting dynamics is defined on a Hilbert space isomorphic to the one of loop quantum gravity.
Book ChapterDOI
Lectures on Loop Quantum Gravity
TL;DR: The Loop Quantum Gravity (LQG) theory as mentioned in this paper is a mathematically rigorous candidate quantum field theory of the gravitational field, which has been shown to have background independence and minimality of structures.
Journal ArticleDOI
Loop-quantum-gravity vertex amplitude
TL;DR: This work presents an alternative dynamics that can be derived as a quantization of a Regge discretization of Euclidean general relativity, where second class constraints are imposed weakly.
References
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Journal ArticleDOI
Loop Quantum Gravity
TL;DR: A general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity is provided, and a guide to the relevant literature is provided.
Journal ArticleDOI
Relativistic spin networks and quantum gravity
John W. Barrett,Louis Crane +1 more
TL;DR: In this article, a four-dimensional state sum model for quantum gravity based on relativistic spin networks that parallels the construction of three-dimensional quantum gravity from ordinary spin networks was proposed.
Journal ArticleDOI
A Lorentzian signature model for quantum general relativity
John W. Barrett,Louis Crane +1 more
TL;DR: In this paper, a relativistic spin network model for quantum gravity based on the Lorentz group and its q-deformation, the Quantum Lorenttz Algebra, was proposed.
Journal ArticleDOI
Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space
Roberto De Pietri,Laurent Freidel,Laurent Freidel,Kirill Krasnov,Kirill Krasnov,Carlo Rovelli,Carlo Rovelli,Carlo Rovelli +7 more
TL;DR: In this paper, the Barrett-Crane quantum gravity model arises naturally from a theory of this type, but restricted to the homogeneous space S3=SO(4)/SO(3), as a term in its Feynman expansion.
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Spacetime as a Feynman diagram: the connection formulation
TL;DR: In this paper, it was shown that the action of a quantum field theory corresponding to any given spin-foam model in a wide class of gravity models can be derived from the connection formulation of the spinfoam models.