Strict deformation quantization via geometric quantization in the Bieliavsky plane
type: Item
instance of: scholarly article
title: Strict deformation quantization via geometric quantization in the Bieliavsky plane
zbMATH Open document ID: 1474.53324
DOI: 10.1155/2020/6794709
author: P. Hurtado
author: A. Leones
author: John B. Moreno
published in: Abstract and Applied Analysis
publication date: 2021-03-12T00:00:00Z
review text: Summary: Using standard techniques from geometric quantization, we rederive the integral product of functions on \(\mathbb{R}^2\) (non-Euclidian) which was introduced by Pierre Bieliavsky as a contribution to the area of strict quantization. More specifically, by pairing the nontransverse real polarization on the pair groupoid \(\mathbb{R}^2\times \overline{\mathbb{R}}^2\), we obtain the well-defined integral transform. Together with a convolution of functions, which is a natural deformation of the usual convolution of functions on the pair groupoid, this readily defines the Bieliavsky product on a subset of \(L^2\left( \mathbb{R}^2\right)\).
Mathematics Subject Classification ID: 53D55
Mathematics Subject Classification ID: 53D50
Mathematics Subject Classification ID: 81S10
zbMATH DE Number: 7321595
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/6794709
OpenAlex ID: W3081253023
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description: scientific article