Coherent States, Wavelets, and Their Generalizations: A Mathematical Overview (Graduate Texts in Contemporary Physics) - Hardcover

Ali, Syed T.; Antoine, J-P.; Gazeau, J.-P.

Hardcover

ISBN 10: 0387989080 ISBN 13: 9780387989082

Publisher: Springer-Verlag New York Inc., 2000

Synopsis

A survey of the theory of coherent states, wavelets, and some of their generalizations, emphasizing mathematical structures. Starting from the standard theory of coherent states over Lie groups, the authors generalize the formalism by associating coherent states to group representations that are square integrable over a homogeneous space; a further step allows the group context to be dispensed with altogether. The unified background makes transparent otherwise obscure properties of wavelets and of coherent states. Many concrete examples, such as semisimple Lie groups, the relativity group, and several kinds of wavelets, are discussed in detail. The book concludes with physical applications, centering on the quantum measurement problem and the quantum-classical transition. Intended as an introduction to current research for graduate students and others entering the field, the mathematical discussion is self- contained. With its extensive references to the research literature, the book will also be a useful compendium of recent results for physicists and mathematicians already active in the field.

About this title

Review

From the reviews:

"The subject of coherent states and/or wavelets (CS-W) is a hot topic for decades. ... Personally I prefer the book under review to many other ones published before. ... It is clearly written, mathematically sound and well illustrated ... . Short but informative historical remarks in the text additionally guide through the literature. The index is useful too. ... I recommend this book to everyone who wishes to learn CS-W, or already works in the area, or just needs a good reference source." (Vladimir V. Kisil, Zentralblatt MATH, Vol. 1064, 2005)

Synopsis

This book presents a survey of the theory of coherent states, wavelets, and some of their generalizations, emphasizing mathematical structures. The point of view is that both the theories of both wavelets and coherent states can be subsumed into a single analytic structure. Starting from the standard theory of coherent states over Lie groups, the authors generalize the formalism by associating coherent states to group representations that are square integrable over a homogeneous space; a further step allows one to dispense with the group context altogether. In this context, wavelets can be generated from coherent states of the affine group of the real line, and higher-dimensional wavelets arise from coherent states of other groups. The unified background makes transparent otherwise obscure properties of wavelets and of coherent states. Many concrete examples, such as semisimple Lie groups, the relativity group, and several kinds of wavelets, are discussed in detail. The book concludes with physical applications, centering on the quantum measurement problem and the quantum-classical transition.

Intended as an introduction to current research for graduate students and others entering the field, the mathematical discussion is self- contained. With its extensive references to the research literature, the book will also be a useful compendium of recent results for physicists and mathematicians already active in the field.

Edition details

• Publisher: Springer-Verlag New York Inc.
• Publication date: 2000
• Language: English
• ISBN 10: 0387989080
• ISBN 13: 9780387989082
• Binding: Hardcover
• Number of pages: 431