Many-Particle Physics

Contents

• 1. Introductory Material
• 1.1 Harmonic Oscillators and Phonons
• 1.2 Second quantization for Particles
• 1.3 Electron-Phonon Interaction
• 1.4 Spin Hamiltonians
• 1.5 Photons
• 1.6 Pair Distribution Function
• 2. Green's Functions at Zero Temperature
• 2.1 Interaction Representation
• 2.2 S Matrix
• 2.3 Green's Functions
• 2.4 Wick's Theorem
• 2.5 Feynman Diagrams
• 2.6 Vacuum Polarization Graphs
• 2.7 Dyson's Equation
• 2.8 Rules for Constructing Diagrams
• 2.9 Time-Loop S Matrix
• 2.10 Photon Green's Functions
• 3. Nonezero Temperature
• 3.1 Introduction
• 3.2 Matsubara Green's Functions
• 3.3 Retarded and Advanced Green's Functions
• 3.4 Dyson's Equation
• 3.5 Frequency Summation
• 3.6 Linked Cluster Expansions
• 3.7 Real-Time Green's Functions
• 3.8 Kubo Formula for Electrical Conductivity
• 3.9 Other Kubo Formulas
• 4. Exactly Solvable Models
• 5. Homogeneous Electron Gas
• 6. Strong Correlations
• 7. Electron-Phonon Interaction
• 8. dc Conductivities
• 9. Optical Properties of Solids
• 10. Superconductivity
• 11. Superfluids