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Guide To Feynman Diagrams in the Many Body 2ND Edition

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Guide To Feynman Diagrams in the Many Body 2ND Edition Cover

 

Synopses & Reviews

Publisher Comments:

Until this book, most treatments of this topic were inaccessible to nonspecialists. A superb introduction to important areas of modern physics, it covers Feynman diagrams, quasi particles, Fermi systems at finite temperature, superconductivity, vacuum amplitude, Dyson's equation, ladder approximation, and much more. "A great delight to read." — Physics Today. 1974 edition.

Synopsis:

Superb introduction for nonspecialists to important area of modern physics. Feynman's diagrams, quasi particles, Dyson's equation, superconductivity, many other topics. Exercises. ." . . a great delight . . ."--"Physics Today." Second (1974) edition.

Synopsis:

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.

Synopsis:

Until this book, most treatments of this topic were inaccessible to nonspecialists. A superb introduction to important areas of modern physics, it covers Feynman diagrams, quasi particles, Fermi systems at finite temperature, superconductivity, vacuum amplitude, Dyson's equation, ladder approximation, and much more. A great delight to read. — Physics Today. 1974 edition.

Synopsis:

Superb introduction for nonspecialists to important areas of modern physics covers major concepts: Feynman diagrams, quasi particles, Fermi systems at finite temperature, superconductivity, vacuum amplitude, Dyson's equation, ladder approximation, and much more. "A great delight to read." — Physics Today. 1974 edition.

Description:

Includes bibliographical references (p. 414-421) and index.

Table of Contents

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

Product Details

ISBN:
9780486670478
Author:
Mattuck, Richard D.
Publisher:
Dover Publications
Author:
Mattuck, Richard D.
Author:
Physics
Location:
New York :
Subject:
General
Subject:
Physics
Subject:
Mathematics
Subject:
Waves & Wave Mechanics
Subject:
Solid State Physics
Subject:
Mathematical Physics
Subject:
Many-body problem
Subject:
Feynman diagrams
Subject:
Physics-General
Edition Number:
2
Edition Description:
Trade Paper
Series:
Dover Books on Physics & Chemistry
Series Volume:
85
Publication Date:
19920631
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
429
Dimensions:
8.5 x 5.38 in 1.05 lb

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Guide To Feynman Diagrams in the Many Body 2ND Edition New Trade Paper
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Product details 429 pages Dover Publications - English 9780486670478 Reviews:
"Synopsis" by , Superb introduction for nonspecialists to important area of modern physics. Feynman's diagrams, quasi particles, Dyson's equation, superconductivity, many other topics. Exercises. ." . . a great delight . . ."--"Physics Today." Second (1974) edition.

"Synopsis" by ,
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.
"Synopsis" by , Until this book, most treatments of this topic were inaccessible to nonspecialists. A superb introduction to important areas of modern physics, it covers Feynman diagrams, quasi particles, Fermi systems at finite temperature, superconductivity, vacuum amplitude, Dyson's equation, ladder approximation, and much more. A great delight to read. — Physics Today. 1974 edition.
"Synopsis" by ,
Superb introduction for nonspecialists to important areas of modern physics covers major concepts: Feynman diagrams, quasi particles, Fermi systems at finite temperature, superconductivity, vacuum amplitude, Dyson's equation, ladder approximation, and much more. "A great delight to read." — Physics Today. 1974 edition.
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