Communications in Mathematical Physics

, Volume 287, Issue 1, pp 179–209

Gauged Laplacians on Quantum Hopf Bundles


    • 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


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.


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.

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© The Author(s) 2008