Weyl quantization and star products
type: Item
instance of: scholarly article
title: Weyl quantization and star products
zbMATH Open document ID: 0882.58015
DOI: 10.1016/S0393-0440(96)00030-7
author: D. Bowes
author: Keith C. Hannabuss
published in: Journal of Geometry and Physics
publication date: 1998-03-12T00:00:00Z
review text: It is well known that many nonlinear systems arise as the symplectic reductions of some linear ones. The authors construct a canonical star product for a given nonlinear system using the Weyl-Moyal product of its corresponding linear part. Via the same ideas they give an algebraic approach to Berezin quantization.
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 53D50
Mathematics Subject Classification ID: 81S10
zbMATH DE Number: 1036751
zbMATH Keywords: symplectic reductions
zbMATH Keywords: star product
zbMATH Keywords: Weyl-Moyal product
zbMATH Keywords: Berezin quantization
reviewed by: Mircea Puta
MaRDI profile type: Publication
cites work: Group-related coherent states
cites work: On a Hilbert space of analytic functions and an associated integral transform part I
cites work: Deformation theory and quantization. II: Physical applications
cites work: QUANTIZATION
cites work: General concept of quantization
cites work: Toeplitz Operators on the Segal-Bargmann Space
cites work: Quantization of Kahler Manifolds. II
cites work: Quantization of Kähler manifolds. III
cites work: Quantization of Kähler manifolds. IV
cites work: Deformation estimates for the Berezin-Toeplitz quantization
cites work: The Mathematics of Second Quantization
cites work: Q4735825
cites work: Harmonic analysis of the de Rham complex on the sphere.
cites work: Some ideas about quantization
cites work: Q3696183
cites work: Geometric quantization and multiplicities of group representations
cites work: Homogeneous quantization and multiplicities of group representations
cites work: Characters and contact transformations
cites work: ON A PROPERTY OF HIGHEST WEIGHT VECTORS
cites work: Some aspects of normal quantisation
cites work: Fronsdal *-quantization and Fell inducing
cites work: Quantum mechanics and partial differential equations
cites work: Transcending Classical Invariant Theory
cites work: Remarks on Classical Invariant Theory
cites work: Q3346437
cites work: Quantization and unitary representations
cites work: Rieffel induction as generalized quantum Marsden-Weinstein reduction
cites work: Q3785520
cites work: Construction of twisted products for cotangent bundles of classical groups and Stiefel manifolds
cites work: Induced representation of locally compact groups. I
cites work: Reduction of symplectic manifolds with symmetry
cites work: Q3308735
cites work: *-products on \(D^ 1(C)\), \(S^ 2\) and related spectral analysis
cites work: *-products on some Kähler manifolds
cites work: Invariant star products and representations of compact semisimple Lie groups
cites work: Geodesic symmetries and invariant star products on Kähler symmetric spaces
cites work: Star products and quantization of Poisson-Lie groups
cites work: Q5788173
cites work: Coherent states for arbitrary Lie group
cites work: Q3743524
cites work: Mathematical Aspects of the Weyl Correspondence
cites work: COHERENT STATES AND KAHLER MANIFOLDS
cites work: Quantization of Kähler manifolds. I: Geometric interpretation of Berezin's quantization
cites work: Induced representations of C\(^*\)-algebras
cites work: Q5522244
cites work: Q5580943
cites work: Q4003058
description: scientific article; zbMATH DE number 1036751