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Covariant Integral Quantization of the Semi-Discrete SO(3)-Hypercylinder
Version 1
: Received: 21 August 2023 / Approved: 22 August 2023 / Online: 23 August 2023 (08:51:38 CEST)
A peer-reviewed article of this Preprint also exists.
Gazeau, J.-P.; Murenzi, R. Covariant Integral Quantization of the Semi-Discrete SO(3)-Hypercylinder. Symmetry 2023, 15, 2044. Gazeau, J.-P.; Murenzi, R. Covariant Integral Quantization of the Semi-Discrete SO(3)-Hypercylinder. Symmetry 2023, 15, 2044.
Abstract
Covariant integral quantization with rotational symmetry SO(3) is established for the quantum motion on this group manifold, or, alternatively, for Gabor signal analysis on this group. We revisit the action of the related (non-unitary) Weyl-Gabor operator on the Hilbert space of square integrable functions on SO(3) and disclose a set of various properties. By selecting weight functions on the corresponding discrete-continuous phase space, one derives related coherent states and Wigner transform.
Keywords
Covariant Weyl-Heisenberg integral quantization; semi-discrete hypercylinder; coherent states; Weyl-Gabor operator; quantum models on SO(3); Wigner function; phase space portrait
Subject
Physical Sciences, Quantum Science and Technology
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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