A Guide to Feynman Diagrams in the Many-Body Problem: Second Edition"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. 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. |
Contents
Quasi Particles in Fermi Systems | |
Ground State Energy and the Vacuum Amplitude or No particle Propagator | |
BirdsEye View of Diagram Methods in the ManyBody Problem | |
Occupation Number Formalism Second Quantization | |
SelfConsistent Renormalization and the Existence of the Fermi Surface | |
Ground State Energy of Electron Gas and Nuclear Matter | |
Collective Excitations and the TwoParticle Propagator | |
Fermi Systems at Finite Temperature | |
Diagram Methods in Superconductivity | |
Phonons from a ManyBody Viewpoint Reprint | |
Quantum Field Theory of Phase Transitions in Fermi Systems | |
Feynman Diagrams in the Kondo Problem | |
More about Quasi Particles | |
The SingleParticle Propagator ReVisited | |
Dysons Equation Renormalization RPA and Ladder Approximations | |
The Renormalization Group | |
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Common terms and phrases
appendix approximation bubble calculation chap chapter classical collective excitations Coulomb defined density diagrammatically dispersion law divergence Dyson equation effective interaction eigenstates Einstein phonon electron gas elementary excitations evaluated example expression external potential factor Fermi surface Fermi system fermion fermion loop ferromagnetic Fetter and Walecka Feynman diagrams finite temperature Fourier transform free propagator frequency graphs Green’s function ground state energy Hamiltonian Hartree-Fock Hence hole lines imaginary impurity infinite integral ions K-matrix Kondo lifetime magnetic many-body problem many-body system mathematical matrix elements metal method momentum normal Note nuclear matter number of particles obtained occupation number formalism operator pair pair-bubble partial sum partial summation particle propagator particle-hole perturbation expansion perturbation series perturbation theory Phys physical pinball poles probability amplitude quantum mechanics renormalization group result scattering Schrödinger equation second quantization self-consistent self-energy single-particle propagator spin superconducting theorem vacuum amplitude vector vertex wave function yields zero