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Deformation Quantization for Actions of Rd : Memoirs of the American Mathematical Society - Marc A. Rieffel

Deformation Quantization for Actions of Rd

Memoirs of the American Mathematical Society

Paperback Published: January 1993
ISBN: 9780821825754
Number Of Pages: 93

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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.

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
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780821825754
ISBN-10: 0821825755
Series: Memoirs of the American Mathematical Society
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 93
Published: January 1993
Publisher: American Mathematical Society
Country of Publication: US
Dimensions (cm): 25.4 x 18.42  x 0.64
Weight (kg): 0.2

Earn 117 Qantas Points
on this Book