This self-contained introduction discusses the evolution of the notion of coherent states, from the early works of Schrodinger 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.
Table des matières
Part I: Coherent States
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
A propos de l’auteur
Jean-Pierre Gazeau is professor of Physics at the University Diderot Paris 7, France, and a member of the ‘Astroparticles and Cosmology’ Laboratory (CNRS, UMR 7164). Having obtained his academic degrees from Sorbonne University and Pierre-and-Marie Curie University (Paris 6), he spent most of his academic career in Paris and, as invited professor and researcher, in many other places, among them UCLA, Louvain, Montreal, Prague, Newcastle, Rio de Janeiro and Sao Paulo. Professor Gazeau has authored more than 150 scientific publications in Theoretical and Mathematical Physics, mostly devoted to group theoretical methods in physics, coherent states, quantization methods, and number theory for aperiodic systems.
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