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| Preface | |
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| Introduction or "Why Green's Functions?" | |
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| Classical Green's functions | |
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| Linear response of quantum systems | |
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| The simple harmonic oscillator | |
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| Single-particle Green's functions | |
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| Correlation functions | |
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| Semiquantitative considerations | |
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| Summary and plan of the book | |
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| References | |
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| Problems | |
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| Formal Matters | |
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| Double-time Green's functions | |
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| Formal properties | |
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| Single-particle Green's functions | |
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| Higher-order Green's functions | |
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| Kramers-Kr�nig relations | |
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| Fluctuation-dissipation theorem | |
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| Equations of motion for Green's functions | |
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| The thermodynamic potential | |
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| An equation for a single-particle Green's function in an external field | |
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| Summary of results | |
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| References | |
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| Problems | |
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| General Approximations | |
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| Perturbation theory with a single-particle potential | |
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| Perturbation theory for interacting particles | |
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| Time and translational invariance | |
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| A system of weakly interacting fermions | |
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| Self-energy | |
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| The Hartree-Fock approximation | |
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| The Hartree approximation | |
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| The random phase approximation and screening | |
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| Conservation laws and Ward identities | |
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| References | |
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| Problems | |
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| Transport Coefficients of a Metal | |
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| Introduction | |
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| The effect of scattering by impurities | |
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| The electrical conductivity | |
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| References | |
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| Problems | |
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| The Coulomb Gas | |
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| Macroscopic considerations | |
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| Microscopic theory | |
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| References | |
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| Problems | |
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| Landau's Theory of Normal Fermi Liquids | |
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| The neutral liquid | |
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| Microscopic basis of Fermi liquid theory | |
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| The charged Fermi liquid | |
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| References | |
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| Problems | |
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| Electrons and Phonons | |
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| Phonons | |
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| Neutron scattering by the lattice | |
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| Structure factor, Green's functions and sum rule | |
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| The interaction between electrons and phonons in a metal | |
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| Perturbation theory for phonons | |
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| Screening of the electron-phonon interaction | |
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| Migdal's theorem | |
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| Phonon and electron self-energies | |
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| References | |
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| Problems | |
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| Superconductivity | |
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| Introduction | |
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| Instability of the normal state | |
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| Thermodynamics of a superconductor | |
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| Effects of external fields | |
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| Effects of impurities | |
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| Phase of the gap parameter and flux quantization | |
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| Tunnelling of electrons | |
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| References | |
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| Problems | |
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| Superfluidity | |
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| Introduction | |
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| Bose-Einstein condensation | |
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| Microscopic theory of liquid helium | |
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| Theorem of Hugenholtz and Pines | |
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| Low-density Bose gas | |
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| The superfluidity and quantization of circulation | |
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| References | |
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| Problems | |
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| Magnetism | |
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| Introduction | |
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| Molecular field theory | |
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| Green's function approach | |
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| Hubbard model | |
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| References | |
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| Problems | |
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| Disordered Systems | |
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| Introduction | |
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| One impurity in a lattice | |
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| Formalism for many impurities | |
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| The virtual crystal approximation | |
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| The average t-matrix approximation (ATA) | |
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| The coherent potential approximation (CPA) | |
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| Electrical conductivity | |
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| References | |
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| Problems | |
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| Critical Behaviour | |
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| Second-order phase transitions | |
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| Critical exponents | |
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| The sum-over-states and fluctuations | |
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| Perturbation theory for the correlation function | |
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| The renormalization group and critical phenomena | |
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| References | |
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| Problems | |
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| Summary of the Results of Second Quantization | |
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| The Sums of Certain Series | |
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| Subject Index | |