Covariant affine integral quantization(s)

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.
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Jean Pierre Gazeau, Romain Murenzi. Covariant affine integral quantization(s). J.Math.Phys., 2016, 57 (5), pp.052102. ⟨10.1063/1.4949366⟩. ⟨hal-01554995⟩



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