The first, second, and third editions of this book seem to occur at ten year intervals. The intent is to keep the book up-to-date. Many-body theory is a field which continually evolves in time. Journals only publish new results, conferences only invite speakers to report new phenomena, and agencies only fund scientists to do new physics. Today's physics is old hat by tomorrow. Students want to learn new material, and textbooks must be modified to keep up with the times. The early chapters in this book teach the techniques of many-body theory. They are largely unchanged in format. The later chapters apply the techniques to specific problems. The third edition increases the number of applications. New sections have been added, while old sections have been modified to include recent applications. The previous editions were set in type using pre-computer technology. No computer file existed of the prior editions. The publisher scanned the second edition and gave me a disk with the contents. This scan recorded the words accurately and scrambled the equations into unintelligible form. So I retyped the equations using LaTeX. Although tedious, it allowed me to correct the infinite numbers of typographical errors in the previous edition. The earlier typesetting methods did not permit such corrections. The entire book was edited sentence-by- sentence. Most old sections of the book were shortened by editing sentences and paragraphs.
About the First Edition:
`This is a worthy newcomer and will make an excellent teaching text. '
`The book should serve as a valuable contribution to the library of students and researchers in solid state and theoretical physics. '
About the Second Edition:
`Since its first edition, this book has become one of the most popular textbooks in quantum many-body theory, thus guaranteeing the interest of the scientific community in this second edition. '
1: Introductory Material. 1.1. Harmonic Oscillators and Phonons. 1.2. Second Quantization for Particles. 1.3. Electron-Phonon Interactions. 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: 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. 3.7. Real Time Green's Functions. 3.8. Kubo Formula for Electrical Conductivity. 3.9. Other Kubo Formulas. 4: Exactly Solvable Models. 4.1. Potential Scattering. 4.2. Localized State in the Continuum. 4.3. Independent Boson Models. 4.4. Bethe Lattice. 4.5. Tomonaga Model. 4.6. Polaritons. 5: Homogeneous Electron Gas. 5.1. Exchange and Correlation. 5.2. Wigner Lattice. 5.3. Metallic Hydrogen. 5.4. Linear Screening. 5.5. Model Dielectric Functions. 5.6. Properties of the Electron Gas. 5.7. Sum Rules. 5.8. One-Electron Properties. 6: Strong Correlations. 6.1. Kondo Model. 6.2. Single-Site Anderson Model. 6.3. Hubbard Model. 6.4. Hubbard Model: Magnetic Phases. 7: Electron-Phonon Interaction. 7.1. Fröhlich Hamiltonian. 7.2. Small Polaron Theory. 7.3. Heavily Doped Semiconductors. 7.4. Metals. 8: dc Conductivities. 8.1. Electron Scattering by Impurities. 8.2. Mobility of Frölich Polarons. 8.3. Electron-Phonon Relaxation Times. 8.4. Electron-Phonon Interactions in Metals. 8.5. Quantum Boltzmann Equation. 8.6. Quantum Dot Tunneling. 9: Optical Properties of Solids. 9.1. Nearly Free-Electron Systems. 9.2. Wannier Excitons. 9.3. X-Ray Spectra in Metals. 10: Superconductivity. 10.1. Cooper Instability. 10.2. Superconducting Tunneling. 10.3. Strong Coupling Theory. 10.4. Transition Temperature. 11: Superfluids. 11.1. Liquid 4He. 11.2. Liquid 3He. 11.3. Quantum Hall Effects.
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