XXXVI Workshop on Geometric Methods in Physics | 2-8.07.2017 |

VI School on Geometry and Physics | 26-30.06.2017 |

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## Jean-Pierre Gazeau## 2D Covariant Affine Integral Quantization(s)Covariant affine integral quantization of the phase space (plane) X (punctured plane) is studied and applied to the motion of a particle in a punctured plane. We examine the consequences of different quantizer operators built from weight functions on the phase space. To illustrate the procedure, we examine two particulars example of weights. The first one corresponds to choice of coherent state, while the second corresponds to the affine inversion in the punctured plane. The later yields the usual canonical quantization and a quasi-probability distribution (2D affine Wigner function) which is real, marginal in both position and momentum vectors. An interesting application to the quantum rotating frame will be presented. |

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University of Bialystok |

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