2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/220310We 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 pressQuantum AlgebraHigh Energy Physics - TheoryMathematical Physics58B32text