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

Book Description
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 the theories of wavelets and coherent states can both be subsumed into a single mathematical 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. Within the group context, wavelets are coherent states of the affine group of the real line, and higher dimensional wavelets are coherent states of other groups. This unified background makes transparent an entire range of properties of coherent states. Approximately one third of the book is devoted to the subject of wavelets, another third to coherent states and the remaining third to a development of the mathematical tools, including a discussion of abstract multiresolution analysis; tau-wavelets are discussed in the context of quasiperiodic discrete wavelets. Many concrete examples are discussed in detail, using semisimple Lie groups, relativity groups and several kinds of wavelets. Intended as an introduction to current research for graduate students and others entering the field, the book is designed for self study, and the mathematical discussion is self-contained. The treatment does not presume any previous acquaintance with either wavelets or coherent states. 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.


Book Info
Presents a survey of the theory of coherent states, wavelets, and some of their generalizations, emphasizing mathematical structures. DLC: Coherent states.


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