Spin-Foam Models and the Physical Scalar Product

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dc.creatorAlesci, Emanuele
dc.creatorNoui, Karim
dc.creatorSardelli, Francesco
dc.date2008-07-22
dc.date.accessioned2026-07-07T11:45:00Z
dc.date.available2026-07-07T11:45:00Z
dc.descriptionThis 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($Γ$), where $Γ$ is the 4-simplex graph, such that its ma- trix 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. The operator P is usually called the "projector" into physical states and its matrix elements gives the physical scalar product. Therefore, we relate the physical scalar product of Loop Quantum Gravity to vertex amplitudes of some Spin-Foam models. We discuss the possibility to extend the action of P to any cylindrical functions on the space manifold.
dc.description24 pages
dc.identifierhttps://arxiv.org/abs/0807.3561
dc.identifierhttp://arxiv.org/abs/0807.3561
dc.identifierPhys.Rev.D78:104009,2008
dc.identifierdoi:10.1103/PhysRevD.78.104009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/201752
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleSpin-Foam Models and the Physical Scalar Product
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