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Generalized Coherent States and Their Applications

  • Book
  • © 1986

Overview

Authors:
  1. Askold Perelomov

    1. Institute of Theoretical and Experimental Physics, Moscow, USSR

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Part of the book series: Theoretical and Mathematical Physics (TMP)

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Table of contents (28 chapters)

  1. Front Matter

    Pages I-XI
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  2. Introduction

    1. Front Matter

      Pages 1-1
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    2. Introduction

      • Askold Perelomov
      Pages 1-3

  3. Generalized Coherent States for the Simplest Lie Groups

    1. Front Matter

      Pages 5-5
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    2. Standard System of Coherent States Related to the Heisenberg-Weyl Group: One Degree of Freedom

      • Askold Perelomov
      Pages 7-39

    3. Coherent States for Arbitrary Lie Groups

      • Askold Perelomov
      Pages 40-47

    4. The Standard System of Coherent States; Several Degrees of Freedom

      • Askold Perelomov
      Pages 48-53

    5. Coherent States for the Rotation Group of Three-Dimensional Space

      • Askold Perelomov
      Pages 54-66

    6. The Most Elementary Noncompact Non-Abelian Simple Lie Group: SU(1, 1)

      • Askold Perelomov
      Pages 67-83

    7. The Lorentz Group: SO(3, 1)

      • Askold Perelomov
      Pages 84-92

    8. Coherent States for the SO(n, 1) Group: Class-I Representations of the Principal Series

      • Askold Perelomov
      Pages 93-100

    9. Coherent States for a Bosonic System with a Finite Number of Degrees of Freedom

      • Askold Perelomov
      Pages 101-110

    10. Coherent States for a Fermionic System with a Finite Number of Degrees of Freedom

      • Askold Perelomov
      Pages 111-116
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Keywords

About this book

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.

Authors and Affiliations

  • Institute of Theoretical and Experimental Physics, Moscow, USSR

    Askold Perelomov

Bibliographic Information

  • Book Title: Generalized Coherent States and Their Applications

  • Authors: Askold Perelomov

  • Series Title: Theoretical and Mathematical Physics

  • DOI: https://doi.org/10.1007/978-3-642-61629-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1986

  • Hardcover ISBN: 978-3-540-15912-4Published: 01 August 1986

  • Softcover ISBN: 978-3-642-64891-5Published: 11 August 2012

  • eBook ISBN: 978-3-642-61629-7Published: 06 December 2012

  • Series ISSN: 1864-5879

  • Series E-ISSN: 1864-5887

  • Edition Number: 1

  • Number of Pages: XI, 320

  • Topics: Quantum Physics, Quantum Information Technology, Spintronics

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