Communications in Mathematical Physics

, Volume 287, Issue 1, pp 179–209

Gauged Laplacians on Quantum Hopf Bundles

Authors

    • Dipartimento di Matematica e InformaticaUniversità di Trieste
    • INFN
  • Cesare Reina
    • Scuola Internazionale Superiore di Studi Avanzati
  • Alessandro Zampini
    • Institut für Angewandte MathematikUniversität Bonn
    • Max Planck Institut für Mathematik

DOI: 10.1007/s00220-008-0672-5

Abstract

We study gauged Laplacian operators on line bundles on a quantum 2-dimensional sphere. Symmetry under the (co)-action of a quantum group allows for their complete diagonalization. These operators describe ‘excitations moving on the quantum sphere’ in the field of a magnetic monopole. The energies are not invariant under the exchange monopole/antimonopole, that is under inverting the direction of the magnetic field. There are potential applications to models of quantum Hall effect.

Acknowledgments

This work was partially supported by the ‘Italian project Cofin06 - Noncommutative geometry, quantum groups and applications’. The research of AZ started at SISSA (Trieste, Italy) and went on at the IAM at Bonn University (Germany), thanks to a fellowship by the Alexander von Humboldt Stiftung; he thanks the Mathematical Physics Sector of SISSA and his host in Germany, Prof. Sergio Albeverio, for their warm hospitality. We thank Francesco D’Andrea for reading the comptu-script.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Copyright information

© The Author(s) 2008