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

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

2007-05-14

arxiv.org/abs/0705.1998v2

Theor. Math. Phys. 155 (2008) 646-658

Physics

Mathematical Physics

15 pages, minor correction and updated references in v2

Scientific paper

10.1007/s11232-008-0054-3

Classical and quantum Hamiltonian reductions of free geodesic systems of complete Riemannian manifolds are investigated. The reduced systems are described 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 meeting all orbits orthogonally in the configuration space. Hyperpolar actions on Lie groups and on symmetric spaces lead to families of integrable systems of spin Calogero-Sutherland type.

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