Harmonic Analysis on Lagrangian Manifolds of Integrable Hamiltonian Systems

Abstract

For an integrable Hamiltonian system we construct a representation of the phase space symmetry algebra over the space of functions on a Lagrangian manifold. The representation is a result of the canonical quantization of the integrable system using separating variables. The variables are chosen in such way that half of them parameterizes the Lagrangian manifold, which coincides with the Liouville torus of the integrable system. The obtained representation is indecomposable and non-exponentiated.