Quantisation of Lie-Poisson manifolds

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dc.creatorRacaniere, Sebastien
dc.date2004-11-03
dc.date.accessioned2026-07-07T05:13:55Z
dc.date.available2026-07-07T05:13:55Z
dc.descriptionIn quantum physics, the operators associated with the position and the momentum of a particle are unbounded operators and $C^*$-algebraic quantisation does therefore not deal with such operators. In the present article, I propose a quantisation of the Lie-Poisson structure of the dual of a Lie algebroid which deals with a big enough class of functions to include the above mentioned example. As an application, I show with an example how the quantisation of the dual of the Lie algebroid associated to a Poisson manifold can lead to a quantisation of the Poisson manifold itself. The example I consider is the torus with constant Poisson structure, in which case I recover its usual $C^*$-algebraic quantisation.
dc.description34 pages
dc.identifierhttps://arxiv.org/abs/math/0411066
dc.identifierhttp://arxiv.org/abs/math/0411066
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73091
dc.subjectDifferential Geometry
dc.subjectMathematical Physics
dc.subjectSymplectic Geometry
dc.subject81S10; 53D55
dc.titleQuantisation of Lie-Poisson manifolds
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