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Superb introduction for nonspecialists covers Feynman diagrams, quasi particles, Fermi systems at finite temperature, superconductivity, vacuum amplitude, Dyson's equation, ladder approximation, more. "A great delight." -- "Physics Today." 1974 edition.

Tabla de contenidos provista por Syndetics

• 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 case
• 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 matter
• 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 group
• 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