This article is cited in 9 papers

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

L. Feher^ab, B. G. Pusztai<sup>cd

a</sup> University of Szeged
^b KFKI Research Institute for Particle and Nuclear Physics
^c Université de Montréal
^d Concordia University, Department of Mathematics and Statistics

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.

Keywords: Hamiltonian reduction, polar action, integrable system.

DOI: 10.4213/tmf6201

 English version: Theoretical and Mathematical Physics, 2008, 155:1, 646–658

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