Covariant affine integral quantization(s), Jean-Pierre Gazeau and Romain Murenzi

ABSTRACT

Covariant affine integral quantization of the half-plane is studied and applied to the motion of a particle on the half-line. We examine the consequences of different quantizer operators built from weight functions on the half-plane. To illustrate the procedure, we examine two particular choices of the weight function, yielding thermal density operators and affine inversion, respectively. The former gives rise to a temperature-dependent probability distribution on the half-plane whereas the latter yields the usual canonical quantization and a quasi-probability distribution (affine Wigner function) which is real, marginal in both momentum p and position q. Journal of Mathematical Physics 57, 052102 (2016).

https://aip.scitation.org/doi/abs/10.1063/1.4949366

https://arxiv.org/abs/1911.00578