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Hamiltonian reductions of free particles under polar actions of compact Lie groups

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Abstract

We investigate classical and quantum Hamiltonian reductions of free geodesic systems of complete Riemannian manifolds. We describe the reduced systems under the assumption that the underlying compact symmetry group acts in a polar manner in the sense that there exist regularly embedded, closed, connected submanifolds intersecting all orbits orthogonally in the configuration space. Hyperpolar actions on Lie groups and on symmetric spaces lead to families of integrable systems of the spin Calogero-Sutherland type.

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Authors and Affiliations

  1. Department of Theoretical Physics, MTA KFKI RMKI, Budapest, Hungary

    L. Fehér

  2. Department of Theoretical Physics, University of Szeged, Szeged, Hungary

    L. Fehér

  3. Centre de Recherches Mathématiques, Université de Montréal, Montreal, Quebec, Canada

    B. G. Pusztai

  4. Department of Mathematics and Statistics, Concordia University, Montreal, Quebec, Canada

    B. G. Pusztai

Authors
  1. L. Fehér
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  2. B. G. Pusztai
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Correspondence to L. Fehér.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 1, pp. 161–176, April, 2008.

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Fehér, L., Pusztai, B.G. Hamiltonian reductions of free particles under polar actions of compact Lie groups. Theor Math Phys 155, 646–658 (2008). https://doi.org/10.1007/s11232-008-0054-3

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