The Fuzzy Sphere: Star Product Induced From Generalized Squeezed States

Details The Fuzzy Sphere: Star Product Induced From Generalized Squeezed States The Fuzzy Sphere: Star Product Induced From Generalized Squeezed States

2004-06-12

arxiv.org/abs/hep-th/0406109v2

Phys.Rev. D71 (2005) 045012

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, version to appear in PRD

Scientific paper

10.1103/PhysRevD.71.045012

A family of states built from the uncertainty principle on the fuzzy sphere has been shown to reproduce the stereographic projection in the large $j$ limit. These generalized squeezed states are used to construct an associative star product which involves a finite number of derivatives on its primary functional space. It is written in terms of a variable on the complex plane. We show that it actually coincides with the one found by H.Gross and P.Presnajder in the simplest cases, endowing the later with a supplementary physical interpretation. We also show how the spherical harmonics emerge in this setting.

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