Communications in Mathematical Physics

, Volume 287, Issue 1, pp 179–209 | Cite as

Gauged Laplacians on Quantum Hopf Bundles

Open Access


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.


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Copyright information

© The Author(s) 2008

Authors and Affiliations

  • Giovanni Landi
    • 1
    • 2
  • Cesare Reina
    • 3
  • Alessandro Zampini
    • 4
    • 5
  1. 1.Dipartimento di Matematica e InformaticaUniversità di TriesteTriesteItaly
  2. 2.INFNTriesteItaly
  3. 3.Scuola Internazionale Superiore di Studi AvanzatiTriesteItaly
  4. 4.Institut für Angewandte MathematikUniversität BonnBonnGermany
  5. 5.Max Planck Institut für MathematikBonnGermany

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