The Fuzzy Sphere Star-Product and Spin Networks

Details The Fuzzy Sphere Star-Product and Spin Networks The Fuzzy Sphere Star-Product and Spin Networks

2001-03-09

arxiv.org/abs/hep-th/0103070v1

J.Math.Phys. 43 (2002) 1737-1754

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, many figures

Scientific paper

10.1063/1.1456255

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.

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