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.

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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.

Conflicts of Interest

The authors declare no conflicts of interest.

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