Coherent States in Quantum Physics

Part I: Coherent States1. Introduction2. The Standard Coherent States: The Basics3. The Standard Coherent States: The (Elementary) Mathematics4. Coherent States in Quantum Information: An Example of Experimental Manipulation5. Coherent States: A General Construction6. The Spin Coherent States7. Selected Pieces of Applications of Standard and Spin Coherent States8. SU(1,1) or SL(2,R)Coherent States9. Another Family of SU(1,1) Coherent States for Quantum Systems10. Squeezed States and their SU(1,1) Content11. Fermionic Coherent StatesPart II: Coherent State Quantization12. Standard Coherent Quantization: The Klauder-Berezin Approach13. Coherent State or Frame Quantization14. CS Quantization of Finite Set, Unit Interval, and Circle15. CS Quantization of Motions on Circle, Interval, and Others16. Quantization of the Motion on the Torus17. Fuzzy Geometries: Sphere and Hyperboloid18. Conclusion and OutlookAppendicesA. The Basic Formalism of Probability TheoryB. The Basics of Lie Algebra, Lie Groups, and their RepresentationC. SU(2)-MaterialD. Wigner-Eckart Theorem for CS quantized Spin HarmonicsE. Symmetrization of the CommutatorBibliography

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.