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

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

2001-12-14

arxiv.org/abs/quant-ph/0112083v2

Physics

Quantum Physics

8 pages

Scientific paper

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

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