PHY 509 Introduction to Non-Relativistic Many Body Systems

Semester: Fall (alternate years)
Credit Hours: 4
Prerequisite: PHY 407, PHY 408, or equivalent

The basic concepts and techniques of many body systems and how they are used to ectract their physical properties. Techniques to be covered are second quantization, Green's functions, linear response theory, perturbative expansions based on Feynman diagrams, variational methods, and functional methods. Electron gas and other normal Fermi systems, Superconductivity, Interacting Bose systems and condensation, Quantum magnetic systems, Localization, etc.

syllabus

1. Number representation: operators and fields for Bose and Fermi systems.

2. Mean field theories: Hartree, Hartree-Fock, Thomas-Fermi approximations; application to atomic systems.

3. Random Phase Approximation (RPA) and collectivity: plasma oscillations.

4. Pairing and quasiparticles for Fermi and Bose systems:
   • Fermi gas with attractive interaction: BCS and quasiparticle theories.
   • Bose gas with weak repulsive interaction: Bogoliubov method.

5. Time development and diagrammatic perturbation theory.

6. Feynman and Goldstone diagrams.

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