Spin-foam models and the physical scalar product
- Laboratoirede Physique, ENS Lyon, CNRS UMR 5672, 46 Allee d'Italie, 69007 Lyon (France)
- Laboratoire de Mathematiques et de Physique Theorique, Parc de Grammont, 37200 Tours (France)
This paper aims at clarifying the link between loop quantum gravity and spin-foam models in four dimensions. Starting from the canonical framework, we construct an operator P acting on the space of cylindrical functions Cyl({gamma}), where {gamma} is the four-simplex graph, such that its matrix elements are, up to some normalization factors, the vertex amplitude of spin-foam models. The spin-foam models we are considering are the topological model, the Barrett-Crane model, and the Engle-Pereira-Rovelli model. If one of these spin-foam models provides a covariant quantization of gravity, then the associated operator P should be the so-called ''projector'' into physical states and its matrix elements should give the physical scalar product. We discuss the possibility to extend the action of P to any cylindrical functions on the space manifold.
- OSTI ID:
- 21250910
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 78, Issue 10; Other Information: DOI: 10.1103/PhysRevD.78.104009; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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