Generalized Coherent States and Their Applications

I Generalized Coherent States for the Simplest Lie Groups.- 1. Standard System of Coherent States Related to the Heisenberg-Weyl Group: One Degree of Freedom.- 2. Coherent States for Arbitrary Lie Groups.- 3. The Standard System of Coherent States; Several Degrees of Freedom.- 4. Coherent States for the Rotation Group of Three-Dimensional Space.- 5. The Most Elementary Noneompact, Non-Abelian Simple Lie Group: SU(1,1).- 6. The Lorentz Group: SO(3,1).- 7. Coherent States for the SO(n, 1) Group: Class-1 Representations of the Principal Series.- 8. Coherent States for a Bosonic System with Finite Number of Degrees of Freedom.- 9. Coherent States for a Fermionic System with Finite Number of Degrees of Freedom.- II General Case.- 10. Coherent States for Nilpotent Lie Groups.- 11. Coherent States for Compact Semisimple Lie Groups.- 12. Discrete Series of Representations: The General Case.- 13. Coherent States for Real Semisimple Lie Groups: Class-I Representations of Principal Series.- 14. Coherent States and Discrete Subgroups: The Case of SU(1,1).- 15. Coherent States for Discrete Series and Discrete Subgroups: General Case.- 16. Coherent States and Berezin's Quantization.- III Physical Applications.- 17. Preliminaries.- 18. Quantum Oscillators.- 19. Particles in External Electromagnetic Fields.- 20. Generating Function for Clebsch-Gordan Coefficients of the SU(2) group.- 21. Coherent States and the Quasiclassical Limit.- 22. 1/N Expansion for Gross-Neveu Models.- 23. Relaxation to Thermodynamic Equilibrium.- 24. Landau Diamagnetism.- 25. The Heisenberg-Euler Lagrangian.- 26. Synchrotron Radiation.- 27. Classical and Quantal Entropy.- Appendix A. Proof of Completeness for Certain CS Subsystems.- Appendix B. Matrix Elements of the Operator D(y).- Appendix C. Jacobians ofGroup Transformations for Classical Domains.- Further Applications of the CS Method.- References.- Subject-Index.- Addendum. Further Applications of the CS Method.- References.- References to Addendum.- Subject-Index.