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Generalized coherent state approach to star products and applications to the fuzzy sphere. (English) Zbl 1097.81537
Summary: We construct a star product associated with an arbitrary two-dimensional Poisson structure using generalized coherent states on the complex plane. From our approach one easily recovers the star product for the fuzzy torus, and also one for the fuzzy sphere. For the latter we need to define the ‘fuzzy’ stereographic projection to the plane and the fuzzy sphere integration measure, which in the commutative limit reduce to the usual formulae for the sphere.

MSC:
81S10 Geometry and quantization, symplectic methods
46L65 Quantizations, deformations for selfadjoint operator algebras
81R30 Coherent states
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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