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

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 Author Lubo, Musongela Source arXiv.org Content type Text File Format PDF Date of Submission 2004-06-12 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Natural sciences & mathematics ♦ Mathematics ♦ Physics Subject Keyword High Energy Physics - Theory ♦ Mathematical Physics ♦ math ♦ physics:hep-th ♦ physics:math-ph 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. Description Reference: Phys.Rev. D71 (2005) 045012 Educational Use Research Learning Resource Type Article Page Count 14