Geometric quantization of completely integrable Hamiltonian systems in the action-angle variables

摘要

We provide geometric quantization of a completely integrable Hamiltoniansystem in the action-angle variables around an invariant torus with respect topolarization spanned by almost-Hamiltonian vector fields of angle variables.The associated quantum algebra consists of functions affine in actioncoordinates. We obtain a set of its nonequivalent representations in theseparable pre-Hilbert space of smooth complex functions on the torus whereaction operators and a Hamiltonian are diagonal and have countable spectra.