Quantum group gauge theory on quantum spaces

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 $S{U}_q(2)$ . 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).

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

References in corpus (1)

• Braided Matrix Structure of the Sklyanin Algebra and of the Quantum Lorentz Group

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