ar X iv : m at h / 04 11 06 6 v 1 [ m at h . D G ] 3 N ov 2 00 4 QUANTISATION OF LIE - POISSON MANIFOLDS
نویسنده
چکیده
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. CONTENTS Acknowledgement 1
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