This monograph treats an extensively developed field in modern
mathematical physics - the theory of generalized coherent states
and their applications to various physical problems. Coherent
states, introduced originally by Schrodinger and von Neumann, were
later employed by Glauber for a quantal description of laser light
beams. The concept was generalized by the author for an arbitrary
Lie group. In the last decade the formalism has been widely applied
to various domains of theoretical physics and mathematics. The area
of applications of generalized coherent states is very wide, and a
comprehensive exposition of the results in the field would be
helpful. This monograph is the first attempt toward this aim. My
purpose was to compile and expound systematically the vast amount
of material dealing with the coherent states and available through
numerous journal articles. The book is based on a number of
undergraduate and postgraduate courses I delivered at the Moscow
Physico-Technical Institute. In its present form it is intended for
professional mathematicians and theoretical physicists; it may also
be useful for university students of mathematics and physics. In
Part I the formalism is elaborated and explained for some of the
simplest typical groups. Part II contains more sophisticated
material; arbitrary Lie groups and symmetrical spaces are
considered. A number of examples from various areas of theoretical
and mathematical physics illustrate advantages of this approach, in
Part III. It is a pleasure for me to thank Dr. Yu. Danilov for many
useful remarks.
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