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Communications in Mathematical Physics

, Volume 157, Issue 3, pp 591–638 | Cite as

Quantum group gauge theory on quantum spaces

  • Thomasz Brzeziński
  • Shahn Majid
Article

Abstract

We construct quantum group-valued canonical connections on quantum homogeneous spaces, including aq-deformed Dirac monopole on the quantum sphere of Podles with quantum differential structure coming from the 3D calculus of Woronowicz onSU q (2). The construction is presented within the setting of a general theory of quantum principal bundles with quantum group (Hopf algebra) fibre, associated quantum vector bundles and connection one-forms. Both the base space (spacetime) and the total space are non-commutative algebras (quantum spaces).

Keywords

Gauge Theory Group Gauge Vector Bundle Hopf Algebra Homogeneous Space 
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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Thomasz Brzeziński
    • 1
  • Shahn Majid
    • 1
  1. 1.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeU.K.

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