Chirality and Dirac operator on noncommutative sphere

Ursula Carow-Watamura, Satoshi Watamura

Research output: Contribution to journalArticlepeer-review

91 Citations (Scopus)


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 languageEnglish
Pages (from-to)365-382
Number of pages18
JournalCommunications in Mathematical Physics
Issue number2
Publication statusPublished - 1997 Jan 2
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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