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Dirac operators on noncommutative principal circle bundles

TitleDirac operators on noncommutative principal circle bundles
Publication TypeJournal Article
Year of Publication2014
AuthorsSitarz, A, Zucca, A, Dabrowski, L

We study spectral triples over noncommutative principal U(1)-bundles of arbitrary dimension and 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 θ → S2.


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