Dirac operator on noncommutative principal circle bundles

We study spectral triples over noncommutative principal U(1)-bundles of arbitrary dimension and formulate a compatibility condition between the connection and the Dirac operator on the total space and on the base space of the bundle. Examples of low dimensional noncommutative tori are analyzed in mo...

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Bibliographic Details
Published inarXiv.org
Main Authors Dabrowski, Ludwik, Sitarz, Andrzej, Zucca, Alessandro
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 20.11.2013
Subjects
Bundles
Bundling
Deformation
Dimensional analysis
Mathematics - Mathematical Physics
Mathematics - Quantum Algebra
Physics - Mathematical Physics
Toruses
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Summary:We study spectral triples over noncommutative principal U(1)-bundles of arbitrary dimension and formulate a compatibility condition between the connection and the Dirac operator on the total space and on the base space of the bundle. Examples of low dimensional noncommutative tori are analyzed in more detail and all connections found that are compatible with an admissible Dirac operator. Conversely, a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection is exhibited. These examples are extended to the theta-deformed principal U(1)-bundle S^3_\theta -> S^2.
ISSN:2331-8422
DOI:10.48550/arxiv.1305.6185