Convex polytopes and quantization of symplectic manifolds.
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.
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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.