Resume
Etant donné une variété symplectique munie des sous-fibrés Lagrangiens F,G ⊂ TℂM complémentaires, nous considérons des connexions symplectiques distinguées. Ces connexions ∇ sont utilisées pour quantifier les germes de fonctions dans les faisceaux C kF par des opérateurs différentiels dans un fibré quantique en lignes Q, qui est muni d'une connexion ∇Q plate en direction de F. Aux propres choix de ∇, ∇Q et d'une suite c de nombres réels, nous définissons des lois de quantification, qui généralizent les quantifications de Kostant-Souriau, de Weyl ou à l'ordre (anti-)normale.
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Hess, H. (1980). Connections on symplectic manifolds and geometric quantization. In: García, P.L., Pérez-Rendón, A., Souriau, J.M. (eds) Differential Geometrical Methods in Mathematical Physics. Lecture Notes in Mathematics, vol 836. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089731
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DOI: https://doi.org/10.1007/BFb0089731
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