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22
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
PonzanoRegge model revisited. III: Feynman diagrams and effective field theory
"... We study the no gravity limit GN → 0 of the PonzanoRegge amplitudes with massive particles and show that we recover in this limit Feynman graph amplitudes (with Hadamard propagator) expressed as an abelian spin foam model. We show how the GN expansion of the PonzanoRegge amplitudes can be resummed ..."
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Cited by 52 (4 self)
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We study the no gravity limit GN → 0 of the PonzanoRegge amplitudes with massive particles and show that we recover in this limit Feynman graph amplitudes (with Hadamard propagator) expressed as an abelian spin foam model. We show how the GN expansion of the PonzanoRegge amplitudes can be resummed. This leads to the conclusion that the effective dynamics of quantum particles coupled to quantum 3d gravity can be expressed in terms of an effective new non commutative field theory which respects the principles of doubly special relativity. We discuss the construction of Lorentzian spin foam models including Feynman propagators.
2Categorical Poincaré representations and state sum applications
, 2008
"... This is intended as a selfcontained introduction to the representation theory developed in order to create a Poincaré 2category state sum model for Quantum Gravity in 4 dimensions. We review the structure of a new representation 2category appropriate to Lie 2group symmetries and discuss its appl ..."
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Cited by 20 (0 self)
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This is intended as a selfcontained introduction to the representation theory developed in order to create a Poincaré 2category state sum model for Quantum Gravity in 4 dimensions. We review the structure of a new representation 2category appropriate to Lie 2group symmetries and discuss its application to the problem of finding a state sum model for Quantum Gravity. There is a remarkable richness in its details, reflecting some desirable characteristics of physical 4dimensionality. We begin with a review of the method of orbits in Geometric Quantization, as an aid to the intuition that the geometric picture unfolded here may be seen as a categorification of this process.
Quantum deformation of two fourdimensional spin foam models
, 2010
"... We construct the qdeformed version of two fourdimensional spin foam models, the Euclidean and Lorentzian versions of the EPRL model. The qdeformed models are based on the representation theory of two copies of Uq(su(2)) at a root of unity and on the quantum Lorentz group with a real deformation ..."
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Cited by 16 (1 self)
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We construct the qdeformed version of two fourdimensional spin foam models, the Euclidean and Lorentzian versions of the EPRL model. The qdeformed models are based on the representation theory of two copies of Uq(su(2)) at a root of unity and on the quantum Lorentz group with a real deformation parameter. For both models we give a definition of the quantum EPRL intertwiners, study their convergence and braiding properties and construct an amplitude for the foursimplexes. We find that both of the resulting models are convergent. 1
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.
CAUSAL SITES AS QUANTUM GEOMETRY
, 2005
"... Abstract. We propose a structure called a causal site to use as a setting for quantum geometry, replacing the underlying point set. The structure has an interesting categorical form, and a natural “tangent 2bundle, ” analogous to the tangent bundle of a smooth manifold. Examples with reasonable fin ..."
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Cited by 4 (0 self)
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Abstract. We propose a structure called a causal site to use as a setting for quantum geometry, replacing the underlying point set. The structure has an interesting categorical form, and a natural “tangent 2bundle, ” analogous to the tangent bundle of a smooth manifold. Examples with reasonable finiteness conditions have an intrinsic geometry, which can approximate classical solutions to general relativity. We propose an approach to quantization of causal sites as well.
String Theory and Quantum Spin Networks, preprint hepth/0307141
"... We propose an approach to formulating string theory in a curved spacetime, which is based on the connection between the states of the WZW model for the isometry group of a background spacetime metric and the representations of the corresponding quantum group. In this approach the string states scatt ..."
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We propose an approach to formulating string theory in a curved spacetime, which is based on the connection between the states of the WZW model for the isometry group of a background spacetime metric and the representations of the corresponding quantum group. In this approach the string states scattering amplitudes are defined by certain evaluations of the theta spin networks for the associated quantum group. These evaluations are given by the spin network invariants defined by the spin foam state sum model associated to the twodimensional BF theory for the background isometry group. We show that the spin foam string amplitudes are well defined in the case of compact manifold spacetimes which admit background group metric, and we compute the simplest scattering amplitudes in the case of the SU(2) background isometry group.