Laplacians and gauged Laplacians on a quantum Hopf bundle
arXiv:1003.5598
Abstract
This paper presents an analysis of the set of connections and covariant derivatives on a U(1) quantum Hopf bundle on the standard Podles sphere, whose total space quantum SU(2) is equipped with the 3d left covariant differential calculus by Woronowicz. The introduction of a Hodge duality on the exterior algebras on both total and base space of the bundle allows for the study of Laplacians and of gauged Laplacians.
59 pages; to appear on "Quantum groups and noncommutative spaces", M.Marcolli and D.Parashar (eds.)