| Preface to second edition |
| Preface to first edition. |
| 0. The Many-Body Problem- for Everybody |
|   | 0.0 What the many-body problem is about |
|   | 0.1 Simple example of non-interacting fictitious bodies |
|   | 0.2 Quasi particles and quasi horses |
|   | 0.3 Collective excitations |
| 1. "Feynman Diagrams, or how to Solve the Many-Body Problem by means of Pictures " |
|   | 1.1 Propagators-the heroes of the many-body problem |
|   | 1.2 Calculating propagators by Feynman diagrams: the drunken man propagator |
|   | 1.3 Propagator for single electron moving through a metal |
|   | 1.4 Single-particle propagator for system of many interacting particles |
|   | 1.5 The two-particle propagator and the particle-hole propagator |
|   | 1.6 The no-particle propagator ('vacuum amplitude') |
| 2. Classical Quasi Particles and the Pinball Propagator |
|   | 2.1 Physical picture of quasi particle |
|   | 2.2 The classical quasi particle propagator |
|   | 2.3 Calculation of the propagator by means of diagrams |
| 3. Quantum Quasi Particles and the Quantum Pinball Propagator |
|   | 3.1 The quantum mechanical propagator |
|   | 3.2 The quantum pinball game |
|   | 3.3 Disappearance of disagreeable divergences |
|   | 3.4 Where the diagram expansion of the propagator really comes from |
|   | 3.5 Energy and lifetime of an electron in an impure metal |
| 4. Quasi Particles in Fermi Systems |
|   | 4.1 Propagator method in many-body systems |
|   | 4.2 Non-interacting Fermi system in external potential; particle-hole picture |
|   | 4.3 A primer of occupation number formalism (second quantization) |
|   | 4.4 Propagator for non-interacting Fermi system in external perturbing potential |
|   | 4.5 Interacting Fermi system |
|   | 4.6 The 'quasi-physical' nature of Feynman diagrams |
|   | 4.7 Hartree and Hartree-Fock quasi particles |
|   | 4.8 Hartree-Fock quasi particles in nuclear matter |
|   | 4.9 "Quasi particles in the electron gas, and the random phase approximation " |
| 5. Ground State Energy and the Vacuum Amplitude or 'No-particle Propagator' |
|   | 5.1 Meaning of the vacuum amplitude. |
|   | 5.2 The pinball machine vacuum amplitude |
|   | 5.3 Quantum vacuum amplitude for one-particle system |
|   | 5.4 Linked cluster theorem for one-particle system |
|   | 5.5 Finding the ground state energy in one-particle system. |
|   | 5.6 The many-body |
| 6. Bird's-Eye View of Diagram Methods in the Many-Body Problem |
| 7. Occupation Number Formalism (Second Quantization) |
|   | 7.1 The advantages of occupation number formalism |
|   | 7.2 Many-body wave function in occupation number formalism |
|   | 7.3 Operators in occupation number formalism |
|   | 7.4 Hamiltonian and Schrödinger equation in occupation number formalism |
|   | 7.5 Particle-hole formalism |
|   | 7.6 Occupation number formalism based on single-particle position eigenstates |
|   | 7.7 Bosons |
| 8. More about Quasi Particles |
|   | 8.1 Introduction |
|   | 8.2 A soluble fermion system: the pure Hartree model |
|   | 8.3 Crude calculation of quasi particle lifetime |
|   | 8.4 General form of quasi particle propagator |
| 9. The Single-Particle Propagator Re-visited |
|   | 9.1 Second quantization and the propagator |
|   | 9.2 Mathematical expression for the single-particle Green's function propagator. |
|   | 9.3 Spectral density function |
|   | 9.4 Derivation of the propagator expansion in the many-body case |
|   | 9.5 Topology of diagrams |
|   | 9.6 Diagram rules for single-particle propagator |
|   | 9.7 "Modified propagator formalism using chemical potential, µ " |
|   | 9.8 Beyond Hartree-Fock: the single pair-bubble approximation |
| 10. "Dyson's Equation, Renormalization, RPA and Ladder Approximations " |
|   | 10.1 General types of partial sums |
|   | 10.2 Dyson's equation |
|   | 10.3 Quasi particles in low-density Fermi system (ladder approximation) |
|   | 10.4 Quasi particles in high-density electron gas (random phase approximation) |
|   | 10.5 The general 'dressed' or 'effective' interaction |
|   | 10.6 The scattering amplitude |
|   | 10.7 Evaluation of the pair bubble; Friedel oscillations |
| 11. Self-Consistent Renormalization and the Existence of the Fermi Surface |
|   | 11.1 "Dressed particle and hole lines, or 'clothed skeletons' " |
|   | 11.2 Existence of quasi particles when the perturbation expansion is valid |
|   | 11.3 Existence of the Fermi surface in an interacting system. |
|   | 11.4 Dressed vertices |
| 12. Ground State Energy of Electron Gas and Nuclear Matter |
|   | 12.1 Review |
|   | 12.2 Diagrams for the ground state energy |
|   | 12.3 Ground state energy of high-density electron gas: theory of Gell-Mann and Brueckner |
|   | 12.4 Brief view of Brueckner theory of nuclear m |
| 13. Collective Excitations and the Two-Particle Propagator |
|   | 13.1 Introduction |
|   | 13.2 The two-particle Green's function propagator |
|   | 13.3 Polarization ('density fluctuation') propagator |
|   | 13.4 Retarded polarization propagator and linear response |
|   | 13.5 The collective excitation propagator |
|   | 13.6 Plasmons and quasi plasmons |
|   | 13.7 Expressing the two-particle propagator in terms of the scattering amplitude |
| 14. Fermi Systems at Finite Temperature |
|   | 14.1 Generalization of the T = 0 case |
|   | 14.2 Statistical mechanics in occupation number formalism |
|   | 14.3 The finite temperature propagator |
|   | 14.4 The finite temperature vacuum amplitude |
|   | 14.5 The pair-bubble at finite temperature |
| 15. Diagram Methods in Superconductivity |
|   | 15.1 Introduction |
|   | 15.2 Hamiltonian for coupled electron-phonon system. |
|   | 15.3 Short review of BCS theory |
|   | 15.4 Breakdown of the perturbation expansion in a superconductor |
|   | 15.5 A brief look at Nambu formalism |
|   | 15.6 Treatment of retardation effects by Nambu formalism |
|   | 15.7 Transition temperature of a superconductor |
| 16. Phonons From a Many-Body Viewpoint (Reprint) |
| 17. Quantum Field Theory of Phase Transitions in Fermi Systems |
|   | 17.1 Introduction |
|   | 17.2 Qualitative theory of phase transitions |
|   | 17.3 Anomalous propagators and the breakdown of the perturbation series in the condensed phase. |
|   | 17.4 The generalized matrix propagator |
|   | 17.5 Application to ferromagnetic phase in system with d-function interaction. |
|   | 17.6 I Divergence of the two-particle propagator and scattering amplitude at the transition point |
| 18. Feynman Diagrams in the Kondo Problem |
|   | 18.1 Introduction |
|   | 18.2 Second-order (Born) approximation. |
|   | 18.3 Parquet approximation with bare propagators. |
|   | 18.4 Self-consistently renormalized s-electrons |
|   | 18.5 Strong-coupling approximation with self-consistently renormalized pseudofermions and vertices. |
| 19. The Renormalization Group |
|   | 19.1 Introduction |
|   | 19.2 Review of effective interaction in the high-density electron gas |
|   | 19.3 Renormalization group for interaction propagators in the high-density electron gas. |
|   | 19.4 Transforming from one transformed quantity to another: the functional equation of the renormaIization g |
|   | 19.5 Lie equation for the renormalization group |
|   | 19.6 Solution of the Lie equation |
|   | Appendices |
|   | A Finding fictitious particles with the canonical transformation. |
|   | A. Dirac formalism |
|   | B. "The time development operator, U(t) . " |
|   | C. Finding the ground state energy from the vacuum amplitude. |
|   | D. "The u(t) operator and its expansion, " |
|   | E. Expansion of the single-particle propagator and vacuum amplitude |
|   | F. Evaluating matrix elements by Wick's theorem. |
|   | G. Derivation of the graphical expansion for propagator and vacuum |
|   | H. The spectral density function |
|   | I. How the id factor is used |
|   | J. Electron propagator in normal electron-phonon system |
|   | K. Spin wave functions. |
|   | L. Sunmary of different kinds of propagators and their spectral representations and analytic properties. . |
|   | M. The decoupled equations of motion for the Green's function expressed as a partial sum of Feyman diagrams |
|   | N. The reduced graph expansion |
|   Answers to Exercises |
|   References |
|   Index |