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46
Spin Foam Models for Quantum Gravity
, 2008
"... In this article we review the present status of the spin foam formulation of nonperturbative (background independent) quantum gravity. The article is divided in two parts. In the first part we present a general introduction to the main ideas emphasizing their motivations from various perspectives. R ..."
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Cited by 123 (7 self)
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In this article we review the present status of the spin foam formulation of nonperturbative (background independent) quantum gravity. The article is divided in two parts. In the first part we present a general introduction to the main ideas emphasizing their motivations from various perspectives. Riemannian 3dimensional gravity is used as a simple example to illustrate conceptual issues and the main goals of the approach. The main features of the various existing models for 4dimensional gravity are also presented here. We conclude with a discussion of important questions to be addressed in four dimensions (gauge invariance, discretization independence, etc.). In the second part we concentrate on the definition of the BarrettCrane model. We present the main results obtained in this framework from a critical perspective. Finally we review the combinatorial formulation of spin foam models based on the dual group field theory technology. We present the BarrettCrane model in this framework and review the finiteness results obtained for both its Riemannian as well
Hamiltonian Analysis of nonchiral Plebanski Theory and its Generalizations
, 809
"... We consider nonchiral, full Lorentz groupbased Plebanski formulation of general relativity in its version that utilizes the Lagrange multiplier field Φ with “internal” indices. The Hamiltonian analysis of this version of the theory turns out to be simpler than in the previously considered in the l ..."
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Cited by 15 (4 self)
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We consider nonchiral, full Lorentz groupbased Plebanski formulation of general relativity in its version that utilizes the Lagrange multiplier field Φ with “internal” indices. The Hamiltonian analysis of this version of the theory turns out to be simpler than in the previously considered in the literature version with Φ carrying spacetime indices. We then extend the Hamiltonian analysis to a more general class of theories whose action contains scalars invariants constructed from Φ. Such theories have recently been considered in the context of unification of gravity with other forces. We show that these more general theories have six additional propagating degrees of freedom as compared to general relativity, something that has not been appreciated in the literature treating them as being not much different from GR. 1
Bimetric theory of gravity from the nonchiral Plebanski action,” Phys
 Rev. D
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Simplicity and closure constraints in spin foam models of gravity
, 802
"... We revise imposition of various constraints in spin foam models of 4dimensional general relativity. We argue that the usual simplicity constraint must be supplemented by a constraint on holonomies and together they must be inserted explicitly into the discretized path integral. At the same time, th ..."
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Cited by 13 (3 self)
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We revise imposition of various constraints in spin foam models of 4dimensional general relativity. We argue that the usual simplicity constraint must be supplemented by a constraint on holonomies and together they must be inserted explicitly into the discretized path integral. At the same time, the closure constraint must be relaxed so that the new constraint expresses covariance of intertwiners assigned to tetrahedra by spin foam quantization. As a result, the spin foam boundary states are shown to be realized in terms of projected spin networks of the covariant loop approach to
Plebanski theory and covariant canonical formulation, Classical Quantum Gravity 24
"... We establish an equivalence between the Hamiltonian formulation of the Plebanski action for general relativity and the covariant canonical formulation of the Hilbert– Palatini action. This is done by comparing the symplectic structures of the two theories through the computation of Dirac brackets. W ..."
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Cited by 11 (3 self)
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We establish an equivalence between the Hamiltonian formulation of the Plebanski action for general relativity and the covariant canonical formulation of the Hilbert– Palatini action. This is done by comparing the symplectic structures of the two theories through the computation of Dirac brackets. We also construct a shifted connection with simplified Dirac brackets, playing an important role in the covariant loop quantization program, in the Plebanski framework. Implications for spin foam models are also discussed. 1
Implementing causality in the spin foam quantum geometry
 Nucl. Phys. B
"... We analyse the classical and quantum geometry of the BarrettCrane spin foam model for four dimensional quantum gravity, explaining why it has to be considering as a covariant realization of the projector operator onto physical quantum gravity states. We discuss how causality requirements can be con ..."
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Cited by 11 (0 self)
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We analyse the classical and quantum geometry of the BarrettCrane spin foam model for four dimensional quantum gravity, explaining why it has to be considering as a covariant realization of the projector operator onto physical quantum gravity states. We discuss how causality requirements can be consistently implemented in this framework, and construct causal transiton amplitudes between quantum gravity states, i.e. realising in the spin foam context the Feynman propagator between states. The resulting causal spin foam model can be seen as a path integral quantization of Lorentzian first order Regge calculus, and represents a link between several approaches to quantum gravity as canonical loop quantum gravity, sumoverhistories formulations, dynamical triangulations and causal sets. In particular, we show how the resulting model can be rephrased within the framework of quantum causal sets (or histories).
Spin Foams and Canonical Quantization
 SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS
, 2012
"... This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the threedimensional context, where the two approaches are in good agreement, we show how the canonical quantization à la Witten of Riemanni ..."
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Cited by 7 (0 self)
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This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the threedimensional context, where the two approaches are in good agreement, we show how the canonical quantization à la Witten of Riemannian gravity with a positive cosmological constant is related to the Turaev–Viro spin foam model, and how the Ponzano–Regge amplitudes are related to the physical scalar product of Riemannian loop quantum gravity without cosmological constant. In the fourdimensional case, we recall a Lorentzcovariant formulation of loop quantum gravity using projected spin networks, compare it with the new spin foam models, and identify interesting relations and their pitfalls. Finally, we discuss the properties which a spin foam model is expected to possess in order to be consistent with the canonical quantization, and suggest a new model illustrating these results.