2-D covariant affine integral quantization(s). Jean-Pierre Gazeau, Tomoi Koide, and Romain Murenzi

Covariant affine integral quantization is studied and applied to the motion of a particle in a punctured plane ℝ2∗:=ℝ2∖{0}, for which the phase space is ℝ2∗×ℝ2. We examine the consequences of different quantizer operators built from weight functions on ℝ2∗×ℝ2. To illustrate the procedure, we examine two examples of weights. The first one corresponds to 2-D coherent state families, while the second one corresponds to the affine inversion in the punctured plane. The later yields the usual canonical quantization and a quasi-probability distribution (2-D affine Wigner function) which is real, marginal in both position 𝐪 and momentum 𝐩.  Advances in Operator Theory (2020), 24 January 2020

https://link.springer.com/article/10.1007/s43036-020-00039-9

https://arxiv.org/abs/1911.00578