Weyl manifold and quantized connection
type: Item
instance of: scholarly article
title: Weyl manifold and quantized connection
zbMATH Open document ID: 0963.53055
author: Akira Yoshioka
published in: Lobachevskii Journal of Mathematics
publication date: 2000-04-09T00:00:00Z
full work available at URL: https://eudml.org/doc/228040
full work available at URL: yoshioka.htm
review text: The subject is a geometric description of deformation quantization, an infinite dimensional Weyl algebra bundle over a symplectic manifold which is called a Weyl manifold. The relation between Weyl manifolds and deformation quantization is reviewed, and also a review is given of the Poincaré-Cartan class which gives the complete classification of Weyl manifolds. A quantized connection or twisted exterior derivative is discussed on a Weyl manifold, where the degree operator field plays an important role. It is shown that the quantized connection coincides with a Fedosov connection in terms of classical coordinates and then it is obtained that the Poincaré-Cartan class is equal to the deRham cohomology class of the curvature of the Fedosov connection.
reviewed by: Akira Yoshioka
Mathematics Subject Classification ID: 53D55
Mathematics Subject Classification ID: 81S10
zbMATH DE Number: 1413880
zbMATH Keywords: deformation quantziation
zbMATH Keywords: Weyl manifold
zbMATH Keywords: Poincaré-Cartan class
zbMATH Keywords: Fedosov connection
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1413880