Chirality and Dirac operator on noncommutative sphere

Ursula Carow-Watamura; Satoshi Watamura

doi:10.1007/BF02506411

Chirality and Dirac operator on noncommutative sphere

Ursula Carow-Watamura, Satoshi Watamura

Research output: Contribution to journal › Article › peer-review

91 Citations (Scopus)

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.

Original language	English
Pages (from-to)	365-382
Number of pages	18
Journal	Communications in Mathematical Physics
Volume	183
Issue number	2
DOIs	https://doi.org/10.1007/BF02506411
Publication status	Published - 1997 Jan 2
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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author = "Ursula Carow-Watamura and Satoshi Watamura",

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AU - Watamura, Satoshi

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Y1 - 1997/1/2

N2 - 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.

AB - 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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Chirality and Dirac operator on noncommutative sphere

Abstract

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