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

Abstract

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.

15 pages, minor correction and updated references in v2

References in corpus (4)

• Spin Calogero models associated with Riemannian symmetric spaces of negative curvature
• Twisted spin Sutherland models from quantum Hamiltonian reduction
• Spinning particles in a Yang-Mills field
• On the self-adjointness of certain reduced Laplace-Beltrami operators

Cited by in corpus (2)

• Twisted spin Sutherland models from quantum Hamiltonian reduction
• Universal Spinning Casimir Equations and Their Solutions