Gauged Laplacians on quantum Hopf bundles

Details Gauged Laplacians on quantum Hopf bundles Gauged Laplacians on quantum Hopf bundles

2008-01-22

arxiv.org/abs/0801.3376v2

Commun.Math.Phys.287:179-209,2009

Mathematics

Quantum Algebra

v2: latex; 32 pages. Papers re-organized; no major changes, several minor ones. Commun. Math. Phys. In press

Scientific paper

10.1007/s00220-008-0672-5

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.

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