Modèles de mousses de spin pour la gravité quantique en 3 dimensions

Abstract : This work presents several new results concerning spin foam model for three-dimensional quantum gravity. Starting from Ponzano-Regge and Turaev-Viro models, we realize a gauge fixing of the diffeomorphism symmetry. Then we introduce point particles in these models, realizing a coupling between quantum gravity and matter. Then we present a new mathematical result on the link between Ponzano-Regge invariant and a Chern-Simons invariant constructed from a quantum group obtained as the double of SU(2). We study the asymptotics of 6j and 10j symbols, which correspond to a semi-classical limit of spin foam models in 3 and 4 dimensions. Finally we show it is possible to realize a non-pertubative sum over topologies of quantum gravity amplitudes in a group field theory framework.
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David Louapre. Modèles de mousses de spin pour la gravité quantique en 3 dimensions. Physique mathématique [math-ph]. Ecole normale supérieure de lyon - ENS LYON, 2004. Français. ⟨tel-00337352⟩

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