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Spin Foams and Canonical Quantization
Alexandrov S., Geiller M., Noui K.
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 08 (2012) 055 - http://hal.archives-ouvertes.fr/hal-00653555
Physique/Relativité Générale et Cosmologie Quantique
Physique/Physique des Hautes Energies - Théorie
Spin Foams and Canonical Quantization
S. Alexandrov ()1, M. Geiller2, K. Noui3
1 :  L2C - Laboratoire Charles Coulomb
CNRS : UMR5221 – Université Montpellier II - Sciences et techniques
1 place Eugène Bataillon Université Montpellier II 34095 Montpellier Cedex 5
2 :  APC - UMR 7164 - AstroParticule et Cosmologie
CNRS : UMR7164 – IN2P3 – Observatoire de Paris – Université Paris VII - Paris Diderot – CEA : DSM/IRFU
APC - UMR 7164, Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, case postale 7020, F-75205 Paris Cedex 13
3 :  LMPT - Laboratoire de Mathématiques et Physique Théorique
Université François Rabelais - Tours – CNRS : UMR7350
Avenue Monge Parc de Grandmont - 37200 Tours
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 three-dimensional 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 four-dimensional case, we recall a Lorentz-covariant 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.

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
non spécifiée
Articles dans des revues avec comité de lecture

88 pages. Invited review for SIGMA Special Issue "Loop Quantum Gravity and Cosmology"

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