English

Quantum group gauge theory on quantum spaces

High Energy Physics - Theory 2009-10-22 v2

Abstract

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

Keywords

Cite

@article{arxiv.hep-th/9208007,
  title  = {Quantum group gauge theory on quantum spaces},
  author = {Tomasz Brzezinski and Shahn Majid},
  journal= {arXiv preprint arXiv:hep-th/9208007},
  year   = {2009}
}

Comments

65 pages DAMTP/92-27 Revised to emphasise more the U(1) monopole example -- includes now full details in the 3D differential calculus

R2 v1 2026-07-22T15:43:30.036Z