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Chirality and Dirac operator on noncommutative sphere

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Abstract

We give a derivation of the Dirac operator on the noncommutative 2-sphere within the framework of the bosonic fuzzy sphere and define Connes' triple. It turns out that there are two different types of spectra of the Dirac operator and correspondingly there are two classes of quantized algebras. As a result we obtain a new restriction on the Planck constant in Berezin's quantization. The map to the local frame in noncommutative geometry is also discussed.

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Authors and Affiliations

  1. Department of Physics, Graduate School of Science, Tohoku University, Aoba-ku, 980-77, Sendai, Japan

    Ursula Carow-Watamura (Fellow of the Japan Society for Promotion of Science) & Satoshi Watamura

Authors
  1. Ursula Carow-Watamura
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  2. Satoshi Watamura
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Communicated by H. Araki

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Carow-Watamura, U., Watamura, S. Chirality and Dirac operator on noncommutative sphere. Commun.Math. Phys. 183, 365–382 (1997). https://doi.org/10.1007/BF02506411

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