Covariant Affine Integral Quantization(s)

Jean Pierre Gazeau; Romain Murenzi

doi:10.1063/1.4949366

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arXiv · 1512.08274

Covariant Affine Integral Quantization(s)

Jean Pierre Gazeau·Romain Murenzi

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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 later 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. 2016-02-06. Covariant Affine Integral Quantization(s). https://doi.org/10.1063/1.4949366

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