Autorentext

Richard D. Mattuck

Klappentext

"A great delight to read."?Physics Today Among the most fertile areas of modern physics, many-body theory has produced a wealth of fundamental results in all areas of the discipline. Unfortunately the subject is notoriously difficult and, until the publication of this book, most treatments of the topic were inaccessible to the average experimenter or non-specialist theoretician. The present work, by contrast, is well within the grasp of the nonexpert. It is intended primarily as a "self-study" book that introduces one aspect of many-body theory, i.e. the method of Feynman diagrams. The book also lends itself to use as a reference in courses on solid state and nuclear physics which make some use of the many-body techniques. And, finally, it can be used as a supplementary reference in a many-body course. Chapters 1 through 6 provide an introduction to the major concepts of the field, among them Feynman diagrams, quasi-particles, and vacuum amplitudes. Chapters 7 through 16 give basic coverage to topics ranging from Dyson's equation and the ladder approximation to Fermi systems at finite temperature and superconductivity. Appendixes summarize the Dirac formalism and include a rigorous derivation of the rules for diagrams. Problems are provided at the end of each chapter and solutions are given at the back of the book. For this second edition, Dr. Mattuck, formerly of the H. C. Orsted Institute and the University of Copenhagen, added to many chapters a new section showing in mathematical detail how typical many-body calculations with Feynman diagrams are carried out. In addition, new exercises were included, some of which gave the reader the opportunity to carry out simpler many-body calculations himself. A new chapter on the quantum field theory of phase transitions rounds out this unusually clear, helpful, and informative guide to the physics of the many-body problem. Unabridged Dover (1992) republication of the second edition published by McGraw-Hill International Book Company.

Inhalt

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
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