It is well known that the representations over an arbitrary configuration
space related to a physical system of the Heisenberg algebra allow to
distinguish the simply and non simply-connected manifolds [arXiv:quant-ph/9908.014,
arXiv:hep-th/0608.023]. In the light of this classification, the dynamics of a
quantum particle on the line is studied in the framework of the conventional
quantization scheme as well as that of the enhanced quantization recently
introduced by J. R. Klauder [arXiv:quant-ph/1204.2870]. The quantum action
functional restricted to the phase space coherent states is obtained from the
enhanced quantization procedure, showing the coexistence of classical and
quantum theories, a fundamental advantage offered by this new approach. The
example of the one dimensional harmonic oscillator is given. Next, the spectrum
of a free particle on the two-sphere is recognized from the covariant
diffeomorphic representations of the momentum operator in the configuration
space. Our results based on simple models also point out the already-known link
between interaction and topology at quantum level.
Cite this paper
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