1. Introductory Material
1.1. Harmonic Oscillators and Phonons
1.2. Second Quantization for Particles
1.3. Electron-Phonon Interactions
1.3.1. Interaction Hamiltonian
1.3.2. Localized Electron
1.3.3. Deformation Potential
1.3.4. Piezoelectric Interaction
1.3.5. Polar Coupling
1.4. Spin Hamiltonians
1.4.1. Homogeneous Spin Systems
1.4.2. Impurity Spin Models
1.5. Photons
1.5.1. Gauges
1.5.2. Lagrangian
1.5.3. Hamiltonian
1.6. Pair Distribution Function
Problems
2. Green's Functions at Zero Temperature.
2.1. Interaction Representation
2.1.1. Schr6dinger
2.1.2. Heisenberg
2.1.3. Interaction
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
2.9.1. Six Green's Functions
2.9.2. Dyson's Equation
2.10. Photon Green's Functions
Problems
3. Nonzero Temperatures
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 Summations
3.6. Linked Cluster Expansions
3.6.1. Thermodynamic Potential
3.6.2. Green's Functions
3.7. Real-Time Green's Functions
3.7.1. Wigner Distribution Function
3.8. Kubo Formula for Electrical Conductivity
3.8.1. Transverse Fields, Zero Temperature
3.8.2. Nonzero Temperatures
3.8.3. Zero Frequency
3.8.4. Photon Self-Energy
3.9. Other Kubo Formulas
3.9.1. Pauli Paramagnetic Susceptibility
3.9.2. Thermal Currents and Onsager Relations
3.9.3. Correlation Functions
Problems
4. Exactly Solvable Models
4.1. Potential Scattering
4.1.1. Reaction Matrix
4.1.2. T Matrix
4.1.3. Friedel's Theorem
4.1.4. Impurity Scattering
4.1.5. Ground State Energy
4.2. Localized State in the Continuum
4.3. Independent Boson Models
4.3.1. Solution by Canonical Transformation.
4.3.2. Feynman Disentangling of Operators
4.3.3. Einstein Model
4.3.4. Optical Absorption and Emission
4.3.5. Sudden Switching
……
5. Homogeneous Electron Gas
6. Strong Correlations
7. Electron-Phonon Interaction
8. dc Conductivities
9. Optical Properties of Solids
10. Superconductivity
11. Superfluids
References
Author Index
Subject Index
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