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 S3->S2.
|Titolo:||Dirac operators on noncommutative principal circle bundles|
|Autori:||Dabrowski L.; Sitarz A.; Zucca A.|
|Rivista:||INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS|
|Data di pubblicazione:||2014|
|Digital Object Identifier (DOI):||10.1142/S0219887814500121|
|Appare nelle tipologie:||1.1 Journal article|