# Coherent States in Quantum Physics

1. Edition September 2009

XIV, 344 Pages, Hardcover

35 Pictures*Monograph*

**978-3-527-40709-5**

### Short Description

This book discusses the evolution of the notion of coherent states, from the early works of Schrödinger to the most recent advances, including signal analysis. An integrated and modern approach to the utility of coherent states in many different branches of physics.

This self-contained introduction discusses the evolution of the notion of coherent states, from the early works of Schrödinger to the most recent advances, including signal analysis. An integrated and modern approach to the utility of coherent states in many different branches of physics, it strikes a balance between mathematical and physical descriptions.

Split into two parts, the first introduces readers to the most familiar coherent states, their origin, their construction, and their application and relevance to various selected domains of physics. Part II, mostly based on recent original results, is devoted to the question of quantization of various sets through coherent states, and shows the link to procedures in signal analysis.

1. Introduction

2. The Standard Coherent States: The Basics

3. The Standard Coherent States: The (Elementary) Mathematics

4. Coherent States in Quantum Information: An Example of Experimental Manipulation

5. Coherent States: A General Construction

6. The Spin Coherent States

7. Selected Pieces of Applications of Standard and Spin Coherent States

8. SU(1,1) or SL(2,R)Coherent States

9. Another Family of SU(1,1) Coherent States for Quantum Systems

10. Squeezed States and their SU(1,1) Content

11. Fermionic Coherent States

Part II: Coherent State Quantization

12. Standard Coherent Quantization: The Klauder-Berezin Approach

13. Coherent State or Frame Quantization

14. CS Quantization of Finite Set, Unit Interval, and Circle

15. CS Quantization of Motions on Circle, Interval, and Others

16. Quantization of the Motion on the Torus

17. Fuzzy Geometries: Sphere and Hyperboloid

18. Conclusion and Outlook

Appendices

A. The Basic Formalism of Probability Theory

B. The Basics of Lie Algebra, Lie Groups, and their Representation

C. SU(2)-Material

D. Wigner-Eckart Theorem for CS quantized Spin Harmonics

E. Symmetrization of the Commutator

Bibliography