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Guide To Feynman Diagrams in the Many Body 2ND Editionby Richard D Mattuck
Synopses & ReviewsPublisher Comments:"A great delight to read."—Physics Today Among the most fertile areas of modern physics, manybody 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 nonspecialist theoretician. The present work, by contrast, is well within the grasp of the nonexpert. It is intended primarily as a "selfstudy" book that introduces one aspect of manybody 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 manybody techniques. And, finally, it can be used as a supplementary reference in a manybody course. Chapters 1 through 6 provide an introduction to the major concepts of the field, among them Feynman diagrams, quasiparticles, 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 manybody 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 manybody 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 manybody problem. Unabridged Dover (1992) republication of the second edition published by McGrawHill International Book Company. Synopsis:Superb introduction for nonspecialists covers Feynman diagrams, quasi particles, Fermi systems at finite temperature, superconductivity, vacuum amplitude, Dyson's equation, ladder approximation, and more. "A great delight." — 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. 414421) and index.
Table of ContentsPreface to second edition
Preface to first edition. 0. The ManyBody Problem for Everybody 0.0 What the manybody problem is about 0.1 Simple example of noninteracting fictitious bodies 0.2 Quasi particles and quasi horses 0.3 Collective excitations 1. "Feynman Diagrams, or how to Solve the ManyBody Problem by means of Pictures " 1.1 Propagatorsthe heroes of the manybody problem 1.2 Calculating propagators by Feynman diagrams: the drunken man propagator 1.3 Propagator for single electron moving through a metal 1.4 Singleparticle propagator for system of many interacting particles 1.5 The twoparticle propagator and the particlehole propagator 1.6 The noparticle 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 manybody systems 4.2 Noninteracting Fermi system in external potential; particlehole picture 4.3 A primer of occupation number formalism (second quantization) 4.4 Propagator for noninteracting Fermi system in external perturbing potential 4.5 Interacting Fermi system 4.6 The 'quasiphysical' nature of Feynman diagrams 4.7 Hartree and HartreeFock quasi particles 4.8 HartreeFock 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 'Noparticle Propagator' 5.1 Meaning of the vacuum amplitude. 5.2 The pinball machine vacuum amplitude 5.3 Quantum vacuum amplitude for oneparticle system 5.4 Linked cluster theorem for oneparticle system 5.5 Finding the ground state energy in oneparticle system. 5.6 The manybody case 6. Bird'sEye View of Diagram Methods in the ManyBody Problem 7. Occupation Number Formalism (Second Quantization) 7.1 The advantages of occupation number formalism 7.2 Manybody 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 Particlehole formalism 7.6 Occupation number formalism based on singleparticle 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 SingleParticle Propagator Revisited 9.1 Second quantization and the propagator 9.2 Mathematical expression for the singleparticle Green's function propagator. 9.3 Spectral density function 9.4 Derivation of the propagator expansion in the manybody case 9.5 Topology of diagrams 9.6 Diagram rules for singleparticle propagator 9.7 "Modified propagator formalism using chemical potential, µ " 9.8 Beyond HartreeFock: the single pairbubble 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 lowdensity Fermi system (ladder approximation) 10.4 Quasi particles in highdensity 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. SelfConsistent 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 highdensity electron gas: theory of GellMann and Brueckner 12.4 Brief view of Brueckner theory of nuclear matter 13. Collective Excitations and the TwoParticle Propagator 13.1 Introduction 13.2 The twoparticle 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 twoparticle 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 pairbubble at finite temperature 15. Diagram Methods in Superconductivity 15.1 Introduction 15.2 Hamiltonian for coupled electronphonon 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 ManyBody 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 dfunction interaction. 17.6 I Divergence of the twoparticle propagator and scattering amplitude at the transition point 18. Feynman Diagrams in the Kondo Problem 18.1 Introduction 18.2 Secondorder (Born) approximation. 18.3 Parquet approximation with bare propagators. 18.4 Selfconsistently renormalized selectrons 18.5 Strongcoupling approximation with selfconsistently renormalized pseudofermions and vertices. 19. The Renormalization Group 19.1 Introduction 19.2 Review of effective interaction in the highdensity electron gas 19.3 Renormalization group for interaction propagators in the highdensity 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 singleparticle 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 electronphonon 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 What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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