The Fuzzy Sphere: Star Product Induced From Generalized Squeezed States

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.

14 pages, version to appear in PRD

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• Anyon wave equations and the noncommutative plane
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Cited by in corpus (1)

• A Perturbative Approach to Fuzzifying Field Theories