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J. Govaerts, “Quantisation, Topology and Interactions,” Lecture Notes, Department of Theoretical Physics, School of Physics, The University of New South Wales, Sydney, 2006.

has been cited by the following article:

• TITLE: Conventional and Enhanced Canonical Quantizations, Application to Some Simple Manifolds

  AUTHORS: Gabriel Y. H. Avossevou, Jean V. Hounguevou, Daniel Sabi Takou

  KEYWORDS: Heisenberg Algebra; Conventional Quantization; Enhanced Quantization; Non Simply-Connected Manifolds; Interaction; Topology

  JOURNAL NAME: Journal of Modern Physics, Vol.4 No.11, November 12, 2013

  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.