Explicit formulas for noncommutative deformations of CPN and CHN

We give explicit expressions of a deformation quantization with separation of variables for \documentclass[12pt]{minimal}\begin{document}${\mathbb C}P^N$\end{document}CPN and \documentclass[12pt]{minimal}\begin{document}${\mathbb C}H^N$\end{document}CHN. This quantization method is one of the ways t...

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Bibliographic Details
Published in:Journal of mathematical physics 2012-07, Vol.53 (7)
Main Authors: SAKO, Akifumi, SUZUKI, Toshiya, UMETSU, Hiroshi
Format: Article
Language:English
Subjects:
Deformation
Exact sciences and technology
Manifolds
Mathematical analysis
Mathematical methods in physics
Mathematical models
Mathematics
Physics
Quantization
Representations
Sciences and techniques of general use
Separation
Stars
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Summary:We give explicit expressions of a deformation quantization with separation of variables for \documentclass[12pt]{minimal}\begin{document}${\mathbb C}P^N$\end{document}CPN and \documentclass[12pt]{minimal}\begin{document}${\mathbb C}H^N$\end{document}CHN. This quantization method is one of the ways to perform a deformation quantization of Kähler manifolds, which is introduced by Karabegov. Star products are obtained as explicit formulas in all order in the noncommutative parameter. We also give the Fock representations of the noncommutative \documentclass[12pt]{minimal}\begin{document}${\mathbb C}P^N$\end{document}CPN and \documentclass[12pt]{minimal}\begin{document}${\mathbb C}H^N$\end{document}CHN.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.4731236