Mathematical aspects of Weyl quantization and phase - Dubin, D. A. (World Scientific, 2000)
Includes bibliographical references (p. 519-530) and index
Pt. I. Fundamentals. ch. 1. Background -- ch. 2. Some remarks on classical mechanics -- ch. 3. The bounded model -- ch. 4. The smooth model -- ch. 5. Representations of the CCR -- ch. 6. Probability in quantum mechanics -- ch. 7. Dynamical systems -- ch. 8. Weyl quantization -- pt. II. Quantization and phase. ch. 9. Quantization in polar coordinates -- ch. 10. Phase operators -- ch. 11. The laser model -- ch. 12. Weyl dequantization -- ch. 13. The Moyal product -- ch. 14. Ordered quantization -- ch. 15. Asymptotics -- ch. 16. Measurements
This book analyzes in considerable generality the quantization-dequantization integral transform scheme of Weyl and Wigner, and considers several phase operator theories. It features: a thorough treatment of quantization in polar coordinates; dequantization by a new method of "motes"; a discussion of Moyal algebras; modifications of the transform method to accommodate operator orderings; a rigorous discussion of the Dicke laser model for one mode, fully quantum, in the thermodynamic limit; analysis of quantum phase theories based on the Toeplitz operator, the coherent state operator, the quantized phase space angle, and a sequence of finite rank operators