2-D Covariant Affine Integral Quantization(s) - Archive ouverte HAL
Article Dans Une Revue Adv.Oper.Th. Année : 2020

2-D Covariant Affine Integral Quantization(s)

Résumé

Covariant affine integral quantization is studied and applied to the motion of a particle in a punctured plane R^2_∗=R^2{0, for which the phase space is R^2_∗=R^2{0X 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.

Dates et versions

hal-02423725 , version 1 (25-12-2019)

Identifiants

Citer

Jean Pierre Gazeau, Tomoi Koide, Romain Murenzi. 2-D Covariant Affine Integral Quantization(s). Adv.Oper.Th., 2020, 5, pp.901-935. ⟨10.1007/s43036-020-00039-9⟩. ⟨hal-02423725⟩
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