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| HAL : hal-00653555, version 1 |
| arXiv : 1112.1961 |
| DOI : 10.3842/SIGMA.2012.055 |
| Fiche détaillée |  Récupérer au format |
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| Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 08 (2012) 055 |
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| Spin Foams and Canonical Quantization |
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| S. Alexandrov 1M. Geiller 2 |
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| (08/2012) |
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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 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. |
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| 1 : | Laboratoire Charles Coulomb (L2C) |
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CNRS : UMR5221 – Université Montpellier II - Sciences et techniques |
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| 2 : | AstroParticule et Cosmologie (APC) |
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CNRS : UMR7164 – IN2P3 – Observatoire de Paris – Université Paris VII - Paris Diderot – CEA : DSM/IRFU |
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| 3 : | Laboratoire de Mathématiques et Physique Théorique (LMPT) |
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CNRS : UMR6083 – Université François Rabelais - Tours |
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| APC - THEORIE |
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| Domaine | : | Physique/Relativité Générale et Cosmologie Quantique Physique/Physique des Hautes Energies - Théorie |
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| Lien vers le texte intégral : |
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| http://fr.arXiv.org/abs/1112.1961 |
| hal-00653555, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00653555 | |
| oai:hal.archives-ouvertes.fr:hal-00653555 | |
| Contributeur : L2c Aigle | |
| Déposé pour le compte de : | |
| Soumis le : Lundi 19 Décembre 2011, 16:48:21 | |
| Dernière modification le : Vendredi 21 Septembre 2012, 12:15:21 | |
