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Published in:
2019 | OriginalPaper | Chapter
1D & 2D Covariant Affine Integral Quantizations
Authors : Jean Pierre Gazeau, Romain Murenzi
Published in: Geometric Methods in Physics XXXVI
Publisher: Springer International Publishing
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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.