2004/11/03 by Sébastien Racanière, Sebastien Racaniere, Racaniere, Sebastien
Mathematics · Physics and Astronomy · #53D55 #81S10 #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG) #math-ph #math.DG #math.MP #math.SG #msc:53D55 #msc:81S10
paper · pdf · doi:10.48550/arxiv.math/0411066
34 pages
arxiv created 2004/11/03 · openalex publication_date 2004/11/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 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.