Coherent States, Wavelets, and Their Generalizations
By addebook • Aug 15th, 2008 • Category: Mathematics
Coherent States, Wavelets, and Their Generalizations (Graduate Texts in Contemporary Physics)
Coherent States, Wavelets, and Their Generalizations (Graduate Texts in Contemporary Physics)
By Syed T. Ali, Jean-Pierre Antoine, Jean-Perre Gazeau
Publisher: Springer
Number Of Pages: 418
Publication Date: 1999-12-29
ISBN-10 / ASIN: 0387989080
ISBN-13 / EAN: 9780387989082
Binding: Hardcover
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.
Summary: A demanding work by true experts and enthusiasts
Rating: 4
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.
Free download Links
Please Login or Register to read the rest of this content.
Related Posts
Leave a Reply
You must be logged in to post a comment.
