Coherent States, Wavelets, and Their Generalizations (Graduate Texts in Contemporary Physics) [Hardcover]

Syed T. Ali (Author), J-P Antoine (Author), Jean-Perre Gazeau (Author)

Book Description

ISBN-10: 0387989080 | ISBN-13: 978-0387989082 | Publication Date: December 29, 1999 | Edition: 1

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.

Editorial Reviews

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)

Product Details

• Hardcover: 431 pages
• Publisher: Springer; 1 edition (December 29, 1999)
• Language: English
• ISBN-10: 0387989080
• ISBN-13: 978-0387989082
• Product Dimensions: 9.6 x 6.3 x 1 inches
• Shipping Weight: 1.6 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #2,089,617 in Books (See Top 100 in Books)

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2 of 2 people found the following review helpful:

4.0 out of 5 stars A demanding work by true experts and enthusiasts, October 5, 2007

By 

George Leigh (Brisbane, Australia) - See all my reviews
(REAL NAME)   

This review is from: Coherent States, Wavelets, and Their Generalizations (Graduate Texts in Contemporary Physics) (Hardcover)

The authors of this book are probably the world's most knowledgeable experts on the topic. They have a tremendous enthusiasm for their subject and there is great beauty in the way they present it. Coherent states arise from quantum mechanics and allow the user to take a classical (non-quantum) view of quantum states in physics. Wavelets, on the other hand, arise from signal and image processing and provide a time-frequency view of a signal, showing which frequencies are present in a signal at each time point (or which spatial scales are present in an image at each location). The book ties these two theories together very elegantly, thereby showing the full power of coherent states. The book assumes extensive knowledge of quantum mechanics and pure mathematics, and demands a lot of the reader.