1D & 2D Covariant Affine Integral Quantizations

Abstract

Covariant affine integral quantization of the half-plane

$$\mathbb{R} \times \mathbb{R}_ * ^ + $$

is presented.We examine the consequences of different quantizer operators built from weight functions on the half-plane. One of these weights yields the usual canonical quantization and a quasi-probability distribution (affine Wigner function) which is real, marginal in both position and momentum vectors. An extension to the phase space for the motion of a particle in the punctured plane and its application to the quantum rotating frame are mentioned.