Mattuck, R. D.

A guide to Feynman diagrams in the many-body problem / R.D. Mattuck. - 2nd edition. - New York : Dover Publications, 1992. - xv, 429 p. : ill. ; 22 cm. - Dover books in science and mathematics . - Dover books in science and mathematics .

The many-body problem for everybody -- Feynman diagrams, or how to solve the many-body problem by means of pictures -- Classical quasi particles and the pinball propagator -- Quantum quasi particles and the quantum pinball propagator -- Quasi particles in Fermi systems -- Ground state energy and the vacuum amplitude or 'no-particle propagator' -- Bird's-eye view of diagram methods in the many-body problem -- Occupation number formalism (second quantization) -- More about quasi particles -- The single-particle propagator re-visited -- Dyson's equation, renormalization, RPA and ladder approximation -- Self-consistent renormalization and the existence of the Fermi surface -- Ground state energy of electron gas and nuclear matter -- Collective excitations and the two-particle propagator -- Fermi systems at finite temperature -- Diagram methods in superconductivity -- Phonons from a many-body viewpoint (reprint) -- Quantum field theory of phase transitions in Fermi systems -- Feynman diagrams in the Kondo problem -- The renormalization group -- Appendices -- Answers to exercises.

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 nonspecialist 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 fir 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 give 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.


Many-body problem.
Feynman diagrams.