The Fuzzy Sphere Star-Product and Spin Networks

Abstract

We analyze the expansion of the fuzzy sphere non-commutative product in powers of the non-commutativity parameter. To analyze this expansion we develop a graphical technique that uses spin networks. This technique is potentially interesting in its own right as introducing spin networks of Penrose into non-commutative geometry. Our analysis leads to a clarification of the link between the fuzzy sphere non-commutative product and the usual deformation quantization of the sphere in terms of the star-product.

21 pages, many figures

References in corpus (3)

• Non-commutative World-volume Geometries: Branes on SU(2) and Fuzzy Spheres
• Field Theory on the q-deformed Fuzzy Sphere I
• Noncommutative Regularization for the Practical Man

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