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.
Spin-foam models and the physical scalar product / Alesci, Emanuele; Noui, K; Sardelli, F.. - In: PHYSICAL REVIEW D, PARTICLES, FIELDS, GRAVITATION, AND COSMOLOGY. - ISSN 1550-7998. - 78:10(2008). [10.1103/PhysRevD.78.104009]
Spin-foam models and the physical scalar product
ALESCI, Emanuele;
2008-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.