Overview

This work describes a general construction of a deformation quantization for any Poisson bracket on a manifold which comes from an action of R]d on that manifold. These deformation quantizations are strict, in the sense that the deformed product of any two functions is again a function and that there are corresponding involutions and operator norms. Many of the techniques involved are adapted from the theory of pseudo-differential operators. The construction is shown to have many favorable properties. A number of specific examples are described, ranging from basic ones such as quantum disks, quantum tori, and quantum spheres, to aspects of quantum groups.

Full Product Details

Author:   Marc A. Rieffel
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Volume:   No. 506
Dimensions:   Width: 18.00cm , Height: 0.70cm , Length: 25.50cm
Weight:   0.207kg
ISBN:  

9780821825754

ISBN 10:   0821825755
Pages:   93
Publication Date:   30 December 1993
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

Oscillatory integrals The deformed product Function algebras The algebra of bounded operators Functoriality for the operator norm Norms of deformed deformations Smooth vectors, and exactness Continuous fields Strict deformation quantization Old examples The quantum Euclidean closed disk and quantum quadrant The algebraists quantum plane, and quantum groups References.

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