1307.1785 (Julia Bernatska et al.)

Harmonic analysis on Lagrangian manifolds of integrable Hamiltonian
systems    [PDF]

Julia Bernatska, Petro Holod

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 in terms of separation variables. The variables are chosen in such way that a 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.

View original: http://arxiv.org/abs/1307.1785