Fuzzy Sphere Realized Form Spherical Coordinates

THE noncommutative geometry is developed by A. Connes in mathematics and introduced into superstring theory by E. Witten et. al. in recent years. The coordinates in the space of D-brane are noncommutative in the presence of a background field B. Fuzzy sphere is a very kind of the noncommutative manifold.FIRSTLY we introduce the constructions of deformed coherent states and corresponding star product, some examples given there. Then we give the generalized realization of fuzzy sphere and construct the fuzzy quadric surface . The spherical coordinate operators for fuzzy sphere with the classical limit when are defined in this paper and their commutator can be given. Using the well-studied star product constructed on the complex plane, we obtain the asymptotic property of the commutator, which indicates that the noncommutativity increases or decreases when approaching the polar areas.