Physics – Mathematical Physics
Scientific paper
2010-12-14
Physics
Mathematical Physics
25 pages, LaTeX, substantially rewritten
Scientific paper
We study spectral triples over noncommutative principal U(1) bundles. Basing on the classical situation and the abstract algebraic approach, we propose an operatorial definition for a connection and compatibility between the connection and the Dirac operator on the total space and on the base space of the bundle. We analyze in details the example of the noncommutative three-torus viewed as a U(1) bundle over the noncommutative two-torus and find all connections compatible with an admissible Dirac operator. Conversely, we find a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection.
Dabrowski Ludwik
Sitarz Andrzej
No associations
LandOfFree
Noncommutative circle bundles and new Dirac operators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Noncommutative circle bundles and new Dirac operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Noncommutative circle bundles and new Dirac operators will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-179887