Spelling suggestions: "subject:"geometric quantization"" "subject:"geometric quantitation""
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Quantisation of the Laplacian and a Curved Version of Geometric QuantisationMeyer, Julien 29 August 2016 (has links)
Let (E,h) be a holomorphic, Hermitian vector bundle over a polarized manifold. We provide a canonical quantisation of the Laplacian operator acting on sections of the bundle of Hermitian endomorphisms of E. If E is simple we obtain an approximation of the eigenvalues and eigenspaces of the Laplacian. In the case when the bundle E is the trivial line bundle, we quantise solutions to the heat equation on the manifold. Furthermore we show that geometric quantisation can be seen as the differential of a natural map between two Riemannian manifolds. Motivated by this fact we compute its next order approximation, namely its Hessian. / Option Mathématique du Doctorat en Sciences / info:eu-repo/semantics/nonPublished
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