2-D Covariant Affine Integral Quantization(s)
arXiv:1911.00578 · doi:10.1007/s43036-020-00039-9
Abstract
Covariant affine integral quantization is studied and applied to the motion of a particle in a punctured plane R^2_\ast=R^2\{0}, for which the phase space is R^2_\ast=R^2\{0}X R^2. We examine the consequences of different quantizer operators built from weight functions on this phase space. 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 and momentum.
In the Addendum " Comment on 2-D Covariant Affine Integral Quantization(s)" a few errors have been identified in the article [Adv. Oper. Theory (2020) 5:901-935] and they are corrected. Furthermore, some notations have been modified in order to avoid any confusion