Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Holonomic control operators in quantum completely integrable Hamiltonian
  systems   We provide geometric quantization of a completely integrable Hamiltonian
system in the action-angle variables around an invariant torus with respect to
the angle polarization. The carrier space of this quantization is the
pre-Hilbert space of smooth complex functions on the torus. A Hamiltonian of a
completely integrable system in this carrier space has a countable spectrum. If
it is degenerate, its eigenvalues are countably degenerate. We study
nonadiabatic perturbations of this Hamiltonian by a term depending on classical
time-dependent parameters. It is originated by a connection on the parameter
space, and is linear in the temporal derivatives of parameters. One can choose
it commuting with a degenerate Hamiltonian of a completely integrable system.
Then the corresponding evolution operator acts in the eigenspaces of this
Hamiltonian, and is an operator of parallel displacement along a curve in the
parameter space.

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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph