Covariant Integral Quantization of the Semi-Discrete SO(3)-Hypercylinder

Symmetry is an international, peer-reviewed, open access journal covering research on symmetry/asymmetry phenomena wherever they occur in all aspects of natural sciences. Symmetry is published monthly online by MDPI. On 10 November 2023, it published ‘Covariant Integral Quantization of the Semi-Discrete SO(3)-Hypercylinder’, an article by Jean-Pierre Gazeau and Romain Murenzi. Here is the abstract of the article:

Covariant integral quantization with rotational SO(3) symmetry is established for quantum motion on this group manifold. It can also be applied to Gabor signal analysis on this group. The corresponding phase space takes the form of a discrete-continuous hypercylinder. The central tool for implementing this procedure is the Weyl–Gabor operator, a non-unitary operator that operates on the Hilbert space of square-integrable functions on SO(3). This operator serves as the counterpart to the unitary Weyl or displacement operator used in constructing standard Schrödinger–Glauber–Sudarshan coherent states. We unveil a diverse range of properties associated with the quantizations and their corresponding semi-classical phase-space portraits, which are derived from different weight functions on the considered discrete-continuous hypercylinder. Certain classes of these weight functions lead to families of coherent states. Moreover, our approach allows us to define a Wigner distribution, satisfying the standard marginality conditions, along with its related Wigner transform.

You can read the full article here: https://www.mdpi.com/2073-8994/15/11/2044