Many Particle Physics (Physics of Solids and Liquids)

This comprehensive textbook utilizes Green's functions and the equations derived from them to solve real physical problems in solid-state theoretical physics. Green's functions are used to describe processes in solids and quantum fluids and to address problems in areas such as electron gas, polarons, electron transport, optical response, superconductivity and superfluidity. The updated third edition features several new chapters on different mean-free paths, Hubbard model, Coulomb blockade, and the quantum Hall effect. New sections have been added, while original sections have been modified to include recent applications. This text is ideal for third- or fourth-year graduate students and includes numerous study problems and an extensive bibliography.

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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