JMP  Vol.4 No.11 , November 2013
Conventional and Enhanced Canonical Quantizations, Application to Some Simple Manifolds
ABSTRACT

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
G. Avossevou, J. Hounguevou and D. Takou, "Conventional and Enhanced Canonical Quantizations, Application to Some Simple Manifolds," Journal of Modern Physics, Vol. 4 No. 11, 2013, pp. 1476-1485. doi: 10.4236/jmp.2013.411177.
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