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 . 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).
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