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 acting on the space of cylindrical functions , where 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 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 to any cylindrical functions on the space manifold.
3 More- Received 24 July 2008
DOI:https://doi.org/10.1103/PhysRevD.78.104009
©2008 American Physical Society