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university of Provence - Aix-Marseille I |  |
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university of Provence - Aix-Marseille I | |
| HAL: hal-00524921, version 1 |
| arXiv: 1006.1294 |
| Detailed view |  Export this paper |
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| Classical and Quantum Gravity 27 (2010) 205003 |
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| Physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory |
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| You Ding 1Carlo Rovelli 1 |
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| (2010) |
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| A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In this paper we reconsider the implementation of the constraints that defines the model. We define in a simple way the boundary Hilbert space of the theory, introducing a slight modification of the embedding of the SU(2) representations into the SL(2,C) ones. We then show directly that all constraints vanish on this space in a weak sense. The vanishing is exact (and not just in the large quantum number limit.) We also generalize the definition of the volume operator in the spinfoam model to the Lorentzian signature, and show that it matches the one of loop quantum gravity, as does in the Euclidean case. |
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| 1: | Centre de Physique Théorique (CPT) |
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CNRS : FR2291 – Université de Provence - Aix-Marseille I – Université de la Méditerranée - Aix-Marseille II – Université Sud Toulon Var |
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| Subject | : | Physics/General Relativity and Quantum Cosmology |
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| Fulltext link: |
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| http://fr.arXiv.org/abs/1006.1294 |
| hal-00524921, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00524921 | |
| oai:hal.archives-ouvertes.fr:hal-00524921 | |
| From: Rovelli Carlo | |
| Submitted on: Saturday, 9 October 2010 19:25:17 | |
| Updated on: Saturday, 9 October 2010 19:47:49 | |
