Gauged Laplacians on Quantum Hopf Bundles

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.