Many-Body Theory Exposed!

Propagator Description of Quantum Mechanics in Many-Body Systems

Willem H Dickhoff, Dimitri Van Neck;;;

• Publisher: WSPC
• Year: 2008
• ISBN:
  9789813101319
• Edition: 2
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

This comprehensive textbook on the quantum mechanics of identical particles includes a wealth of valuable experimental data, in particular recent results from direct knockout reactions directly related to the single-particle propagator in many-body theory. The comparison with data is incorporated from the start, making the abstract concept of propagators vivid and accessible. Results of numerical calculations using propagators or Green's functions are also presented. The material has been thoroughly tested in the classroom and the introductory chapters provide a seamless connection with a one-year graduate course in quantum mechanics. While the majority of books on many-body theory deal with the subject from the viewpoint of condensed matter physics, this book emphasizes finite systems as well and should be of considerable interest to researchers in nuclear, atomic, and molecular physics. A unified treatment of many different many-body systems is presented using the approach of self-consistent Green's functions. The second edition contains an extensive presentation of finite temperature propagators and covers the technique to extract the self-energy from experimental data as developed in the dispersive optical model.

The coverage proceeds systematically from elementary concepts, such as second quantization and mean-field properties, to a more advanced but self-contained presentation of the physics of atoms, molecules, nuclei, nuclear and neutron matter, electron gas, quantum liquids, atomic Bose–Einstein and fermion condensates, and pairing correlations in finite and infinite systems, including finite temperature.

Table of contents

• Contents
• Preface
• 1. Identical particles
• 2. Second quantization
• 3. Independent-particle model for fermions in finite systems
• 4. Two-particle states and interactions
• 5. Noninteracting bosons and fermions
• 6. Propagators in one-particle quantum mechanics
• 7. Single-particle propagator in the many-body system
• 8. Perturbation expansion of the single-particle propagator
• 9. Dyson equation and self-consistent Green's functions
• 10. Mean-field or Hartree–Fock approximation
• 11. Beyond the mean-field approximation
• 12. Interacting boson systems
• 13. Excited states in finite systems
• 14. Excited states in infinite systems
• 15. Excited states in N ± 2 systems and in-medium scattering
• 16. Dynamical treatment of the self-energy in infinite systems
• 17. Dynamical treatment of the self-energy in finite systems
• 18. Bogoliubov perturbation expansion for the Bose gas
• 19. Boson perturbation theory applied to physical systems
• 20. In-medium interaction and scattering of dressed particles
• 21. Conserving approximations and excited states
• 22. Pairing phenomena
• 23. Elastic scattering and the self-energy in finite systems
• 24. Finite-temperature formalism and applications
• Appendix A Pictures in quantum mechanics
• Appendix B Practical results from angular momentum algebra
• Bibliography
• Index