2020 Strict Deformation Quantization via Geometric Quantization in the Bieliavsky Plane
P. Hurtado, A. Leones, J. B. Moreno
Author Affiliations +
Abstr. Appl. Anal. 2020: 1-7 (2020). DOI: 10.1155/2020/6794709

Abstract

Using standard techniques from geometric quantization, we rederive the integral product of functions on 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 2ׯ2, 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 L2(2).

Acknowledgments

The authors would like to express their gratitude to Pedro de Magalhães Rios, Thesis advisor of the Mathematics Department of ICMC-São Paulo University, for his critical reading of the manuscript and many valuable suggestions for improvements.

Citation

Download Citation

P. Hurtado. A. Leones. J. B. Moreno. "Strict Deformation Quantization via Geometric Quantization in the Bieliavsky Plane." Abstr. Appl. Anal. 2020 1 - 7, 2020. https://doi.org/10.1155/2020/6794709

Information

Received: 12 April 2020; Accepted: 29 June 2020; Published: 2020
First available in Project Euclid: 28 July 2020

Digital Object Identifier: 10.1155/2020/6794709

Rights: Copyright © 2020 Hindawi

JOURNAL ARTICLE
7 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

Vol.2020 • 2020
Back to Top