Symmetry reduction of Brownian motion and Quantum Calogero-Moser systems

Abstract

Let $Q$ be a Riemannian $G$-manifold. This paper is concerned with the symmetry reduction of Brownian motion in $Q$ and ramifications thereof in a Hamiltonian context. Specializing to the case of polar actions we discuss various versions of the stochastic Hamilton-Jacobi equation associated to the symmetry reduction of Brownian motion and observe some similarities to the Schrödinger equation of the quantum free particle reduction as described by Feher and Pusztai. As an application we use this reduction scheme to derive examples of quantum Calogero-Moser systems from a stochastic setting.

V2 contains some improvements thanks to referees' suggestions; to appear in Stochastics and Dynamics

References in corpus (4)

• Spin Calogero models obtained from dynamical r-matrices and geodesic motion
• Spin Calogero models associated with Riemannian symmetric spaces of negative curvature
• Hamiltonian reductions of free particles under polar actions of compact Lie groups
• Singular cotangent bundle reduction and spin Calogero-Moser systems

Cited by in corpus (1)

• Geometry of non-holonomic diffusion