Variations à la Fourier-Weyl-Wigner on Quantizations of the Plane and the Half-Plane
AbstractAny quantization maps linearly function on a phase space to symmetric operators in a Hilbert space. Covariant integral quantization combines operator-valued measure with the symmetry group of the phase space. Covariant means that the quantization map intertwines classical (geometric operation) and quantum (unitary transformations) symmetries. Integral means that we use all resources of integral calculus, in order to implement the method when we apply it to singular functions, or distributions, for which the integral calculus is an essential ingredient. We first review this quantization scheme before revisiting the cases where symmetry covariance is described by the Weyl-Heisenberg group and the affine group respectively, and we emphasize the fundamental role played by Fourier transform in both cases. As an original outcome of our generalisations of the Wigner-Weyl transform, we show that many properties of the Weyl integral quantization, commonly viewed as optimal, are actually shared by a large family of integral quantizations. View Full-Text
A printed edition of this Special Issue is available here.
Share & Cite This Article
Bergeron, H.; Gazeau, J.-P. Variations à la Fourier-Weyl-Wigner on Quantizations of the Plane and the Half-Plane. Entropy 2018, 20, 787.
Bergeron H, Gazeau J-P. Variations à la Fourier-Weyl-Wigner on Quantizations of the Plane and the Half-Plane. Entropy. 2018; 20(10):787.Chicago/Turabian Style
Bergeron, Hervé; Gazeau, Jean-Pierre. 2018. "Variations à la Fourier-Weyl-Wigner on Quantizations of the Plane and the Half-Plane." Entropy 20, no. 10: 787.
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.