Geometric quantization of a particle in a perpendicular magnetic field
type: Item
instance of: scholarly article
title: Geometric quantization of a particle in a perpendicular magnetic field
zbMATH Open document ID: 1373.53123
author: Guillermo Capobianco
author: Walter Reartes
published in: Journal of Geometry and Symmetry in Physics
publication date: 2017-02-09T00:00:00Z
review text: The authors of this paper study the quantization of a particle in the plane under the influence of a perpendicular magnetic field, using geometric quantization and half-forms in the Hilbert space of holomorphic functions. Relying on a judiciously chosen coordinate transformation they are able to convert the problem into a system of harmonic oscillators. The later problem is solved directly and, as a bonus, the relationship between different representations is highlighted as well. Finally, the authors point out the isomorphism between the holomorphic representation and the standard Schrödinger representation.
Mathematics Subject Classification ID: 53D50
Mathematics Subject Classification ID: 81S10
zbMATH DE Number: 6683085
zbMATH Keywords: geometric quantization
zbMATH Keywords: Landau levels
zbMATH Keywords: Segal-Bargmann transform
reviewed by: Ivaïlo Mladenov
MaRDI profile type: Publication
OpenAlex ID: W2728354871
DOI: 10.7546/JGSP-41-2016-17-32
description: scientific article; zbMATH DE number 6683085