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Quantisation of the Laplacian and a Curved Version of Geometric Quantisation

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

Identiferoai:union.ndltd.org:ulb.ac.be/oai:dipot.ulb.ac.be:2013/235181
Date29 August 2016
CreatorsMeyer, Julien
ContributorsFine, Joel, Gutt, Simone, Bertelson, Mélanie, Ross, Julius, Marinescu, George
PublisherUniversite Libre de Bruxelles, Université libre de Bruxelles, Faculté des Sciences – Mathématiques, Bruxelles
Source SetsUniversité libre de Bruxelles
LanguageEnglish
Detected LanguageEnglish
Typeinfo:eu-repo/semantics/doctoralThesis, info:ulb-repo/semantics/doctoralThesis, info:ulb-repo/semantics/openurl/vlink-dissertation
FormatNo full-text files

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