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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Acknowledgments
This work was partially supported by the ‘Italian project Cofin06 - Noncommutative geometry, quantum groups and applications’. The research of AZ started at SISSA (Trieste, Italy) and went on at the IAM at Bonn University (Germany), thanks to a fellowship by the Alexander von Humboldt Stiftung; he thanks the Mathematical Physics Sector of SISSA and his host in Germany, Prof. Sergio Albeverio, for their warm hospitality. We thank Francesco D’Andrea for reading the comptu-script.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Landi, G., Reina, C. & Zampini, A. Gauged Laplacians on Quantum Hopf Bundles. Commun. Math. Phys. 287, 179–209 (2009). https://doi.org/10.1007/s00220-008-0672-5
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DOI: https://doi.org/10.1007/s00220-008-0672-5