Gauged Laplacians on quantum Hopf bundles

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

References in corpus (6)

• Quantum group gauge theory on quantum spaces
• Projective module description of the q-monopole
• A Local Index Formula for the Quantum Sphere
• Spin-Hall effect with quantum group symmetry
• Line bundles on quantum spheres
• On the noncommutative spin geometry of the standard Podles sphere and index computations

Cited by in corpus (8)

• Anti-selfdual Connections on the Quantum Projective Plane: Monopoles
• Quantum Bundle Description of the Quantum Projective Spaces
• Calculi, Hodge operators and Laplacians on a quantum Hopf fibration
• Dimensional reduction over the quantum sphere and non-abelian q-vortices
• Derivation based differential calculi for noncommutative algebras deforming a class of three dimensional spaces
• Geometric foundations for classical $\mathrm{U}(1)$-gauge theory on noncommutative manifolds
• Noncommutative Kahler Geometry of the Standard Podles Sphere
• Twisted sigma-model solitons on the quantum projective line