title: Convex polytopes and quantization of symplectic manifolds.
abstract: Quantum mechanics associate to some symplectic manifolds M a quantum model Q(M), which is a Hilbert space. The space Q(M) is the quantum mechanical analogue of the classical phase space M. We discuss here relations between the volume of M and the dimension of the vector space Q(M). Analogues for convex polyhedra are considered.
authors.affiliation: Ecole Normale Supérieure et Unité Associée 762 du Centre National de la Recherche Scientifique, Departement de Mathematiques et d'Informatique, Ecole Normale Supérieure, 45 rue d'Ulm, 75005 Paris, France.
authors.forename: M
authors.initials: M
authors.lastname: Vergne