Communications in Mathematical Physics

, Volume 182, Issue 3, pp 579–617

Strong connections on quantum principal bundles

  • Piotr M. Hajac


A gauge invariant notion of a strong connection is presented and characterized. It is then used to justify the way in which a global curvature form is defined. Strong connections are interpreted as those that are induced from the base space of a quantum bundle. Examples of both strong and non-strong connections are provided. In particular, such connections are constructed on a quantum deformation of the two-sphere fibrationS2RP2. A certain class of strongUq(2)-connections on a trivial quantum principal bundle is shown to be equivalent to the class of connections on a free module that are compatible with theq-dependent hermitian metric. A particular form of the Yang-Mills action on a trivialUq(2)-bundle is investigated. It is proved to coincide with the Yang-Mills action constructed by A. Connes and M. Rieffel. Furthermore, it is shown that the moduli space of critical points of this action functional is independent ofq.


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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Piotr M. Hajac
    • 1
  1. 1.Mathematics SectionInternational Centre for Theoretical PhysicsTriesteItaly
  2. 2.Department of Mathematical Methods in PhysicsWarsaw UniversityWarsawPoland

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