QUANTUM GROUP GAUGE-THEORY ON QUANTUM SPACES

We construct quantum group-valued canonical connections on quantum hom ogeneous spaces, including a q-deformed Dirac monopole on the quantum sphere of Podles with quantum differential structure coming from the 3 D calculus of Woronowicz on SU(q)(2). The construction is presented wi thin 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 tot al space are non-commutative algebras (quantum spaces).