Communications in Mathematical Physics

, Volume 287, Issue 1, pp 179-209

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Gauged Laplacians on Quantum Hopf Bundles

  • Giovanni LandiAffiliated withDipartimento di Matematica e Informatica, Università di TriesteINFN Email author 
  • , Cesare ReinaAffiliated withScuola Internazionale Superiore di Studi Avanzati
  • , Alessandro ZampiniAffiliated withInstitut für Angewandte Mathematik, Universität BonnMax Planck Institut für Mathematik


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.