Gauged Laplacians on quantum Hopf bundles
arXiv:0801.3376 · 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.
v2: latex; 32 pages. Papers re-organized; no major changes, several minor ones. Commun. Math. Phys. In press