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.
Author(s): Professor Dr. Askold Perelomov (auth.)
Series: Texts and Monographs in Physics
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 1986
Language: English
Pages: 320
Tags: Quantum Physics;Quantum Information Technology, Spintronics
Front Matter....Pages I-XI
Front Matter....Pages 1-1
Introduction....Pages 1-3
Front Matter....Pages 5-5
Standard System of Coherent States Related to the Heisenberg-Weyl Group: One Degree of Freedom....Pages 7-39
Coherent States for Arbitrary Lie Groups....Pages 40-47
The Standard System of Coherent States; Several Degrees of Freedom....Pages 48-53
Coherent States for the Rotation Group of Three-Dimensional Space....Pages 54-66
The Most Elementary Noncompact Non-Abelian Simple Lie Group: SU (1, 1)....Pages 67-83
The Lorentz Group: SO (3, 1)....Pages 84-92
Coherent States for the SO ( n , 1) Group: Class-I Representations of the Principal Series....Pages 93-100
Coherent States for a Bosonic System with a Finite Number of Degrees of Freedom....Pages 101-110
Coherent States for a Fermionic System with a Finite Number of Degrees of Freedom....Pages 111-116
Front Matter....Pages 117-117
Coherent States for Nilpotent Lie Groups....Pages 119-125
Coherent States for Compact Semisimple Lie Groups....Pages 126-133
Discrete Series of Representations: The General Case....Pages 134-144
Coherent States for Real Semisimple Lie Groups: Class-I Representations of Principal Series....Pages 145-172
Coherent States and Discrete Subgroups: The Case of SU (1, 1)....Pages 173-181
Coherent States for Discrete Series and Discrete Subgroups: General Case....Pages 182-184
Coherent States and Berezin’s Quantization....Pages 185-203
Front Matter....Pages 205-205
Preliminaries....Pages 207-210
Quantum Oscillators....Pages 211-230
Particles in External Electromagnetic Fields....Pages 231-252
Front Matter....Pages 205-205
Generating Function for Clebsch-Gordan Coefficients of the SU (2) Group....Pages 253-255
Coherent States and the Quasiclassical Limit....Pages 256-259
1/ N Expansion for Gross-Neveu Models....Pages 260-269
Relaxation to Thermodynamic Equilibrium....Pages 270-281
Landau Diamagnetism....Pages 282-285
The Heisenberg-Euler Lagrangian....Pages 286-288
Synchrotron Radiation....Pages 289-291
Classical and Quantal Entropy....Pages 292-295
Back Matter....Pages 296-320
