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arXiv · 0801.3376

Gauged Laplacians on quantum Hopf bundles

Giovanni Landi·Cesare Reina·Alessandro Zampini
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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.

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Giovanni Landi, Cesare Reina, Alessandro Zampini. 2008-11-18. Gauged Laplacians on quantum Hopf bundles. https://doi.org/10.1007/s00220-008-0672-5

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