Generalized Coherent State Approach to Star Products and Applications to the Fuzzy Sphere

Details Generalized Coherent State Approach to Star Products and Applications to the Fuzzy Sphere Generalized Coherent State Approach to Star Products and Applications to the Fuzzy Sphere

2000-10-23

arxiv.org/abs/hep-th/0010187v2

Nucl.Phys.B600:531-547,2001

Physics

High Energy Physics

High Energy Physics - Theory

18 pages

Scientific paper

10.1016/S0550-3213(00)00743-4

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.

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