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The Fuzzy Sphere: Star Product Induced From Generalized Squeezed States

Musongela Lubo
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Abstract

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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Musongela Lubo. 2005-02-09. The Fuzzy Sphere: Star Product Induced From Generalized Squeezed States. https://doi.org/10.1103/physrevd.71.045012

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