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.

arXiv comment15 pages, minor correction and updated references in v2

References in corpus (8)

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• Harmony of Spinning Conformal Blocks
• From Spinning Conformal Blocks to Matrix Calogero-Sutherland Models
• Derivations of the trigonometric BC(n) Sutherland model by quantum Hamiltonian reduction
• Twisted spin Sutherland models from quantum Hamiltonian reduction
• Universal Spinning Casimir Equations and Their Solutions
• Introduction to Lie groups, isometric and adjoint actions and some generalizations
• Symmetry reduction of Brownian motion and Quantum Calogero-Moser systems