A Guide to Feynman Diagrams in the Many-Body Problem

Dover Books on Physics

Courier Corporation
2
Free sample

"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.
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Additional Information

Publisher
Courier Corporation
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Published on
Aug 21, 2012
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Pages
464
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ISBN
9780486131641
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Language
English
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Genres
Science / Physics / General
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This content is DRM protected.
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This outstanding volume, designed for junior and senior undergraduates in physics or electrical engineering, is an unusually comprehensive treatment of the subject. The book begins with the basis of electric and magnetic fields and builds up to electromagnetic theory, followed by a number of related and subsidiary topics, including relativity.
Chapter 1 gives a detailed treatment of the del operator with many examples. Chapters 2–7 cover magnetostatics and electrostatics, including Coulomb's law, electrostatic and magnetostatic curl in a vacuum, Gauss's law, electrostatic and magnetostatic divergence in a vacuum, and electrostatics and magnetostatics in matter. Chapter 8 is devoted to three special methods for solving various problems in electrostatics. Chapter 9 deals with metallic conduction, and chapter 10 is concerned with ferromagnetism. Chapter 11 discusses the basic phenomena associated with variations in time. Then chapter 12 treats electric circuits. After chapters on special relativity and the connection between electricity and magnetism, the last five chapters deal with waves of various kinds: plane waves, transmission lines, reflection and refraction, guided waves, and radiation.
In each section of each chapter, there are several worked-out examples, illustrating practical applications of the preceding theory. In addition, each section concludes with a collection of 15 to 20 problems, resulting in a total of over 900 problems in the text, conveniently grouped by subject. Answers for the odd-numbered problems are provided at the back of the book.
Professor Shadowitz (Fairleigh Dickinson University) is well known for his often novel perspective and his ability to bridge the world of the theoretical physicist and the practical electrical engineer. This well-written text, esteemed in the field for its original and interesting material, offers an excellent exhibition of his uncommon pedagogical skills.
Unlike most textbooks on electromagnetic theory, which treat electricity, magnetism, Coulomb's law and Faraday's law as almost independent subjects within the framework of the theory, this well-written text takes a relativistic point of view in which electric and magnetic fields are really different aspects of the same physical quantity.
Suitable for advanced undergraduates and graduate students, this volume offers a superb exposition of the essential unity of electromagnetism in its natural , relativistic framework while demonstrating the powerful constraint of relativistic invariance. It will be seen that all electromagnetism follows from electrostatics and from the requirement for the simplest laws allowable under the relativistic constraint. By means of these insights, the author hopes to encourage students to think about theories as yet undeveloped and to see this model as useful in other areas of physics.
After an introductory chapter establishing the mathematical background of the subject and a survey of some new mathematical ideas, the author reviews the principles of electrostatics. He then introduces Einstein's special theory of relativity and applies it throughout the rest of the book. Topics treated range from Gauss's theorem, Coulomb's law, the Faraday effect and Fresnel's equations to multiple expansion of the radiation field , interference and diffraction, waveguides and cavities and electric and magnetic susceptibility.
Carefully selected problems at the end of each chapter invite readers to test their grasp of the material. Professor Schwartz received his Ph.D. from Columbia University and has taught physics there and at Stanford University. He is perhaps best known for his experimental research in the field of high-energy physics and was a co-discoverer of the muon-type neutrino in 1962. He shared the 1988 Nobel Prize in Physics with Leon M. Lederman and Jack Steinberger.
Analytical mechanics is, of course, a topic of perennial interest and usefulness in physics and engineering, a discipline that boasts not only many practical applications, but much inherent mathematical beauty. Unlike many standard textbooks on advanced mechanics, however, this present text eschews a primarily technical and formalistic treatment in favor of a fundamental, historical, philosophical approach. As the author remarks, there is a tremendous treasure of philosophical meaning" behind the great theories of Euler and Lagrange, Hamilton, Jacobi, and other mathematical thinkers.
Well-written, authoritative, and scholarly, this classic treatise begins with an introduction to the variational principles of mechanics including the procedures of Euler, Lagrange, and Hamilton.
Ideal for a two-semester graduate course, the book includes a variety of problems, carefully chosen to familiarize the student with new concepts and to illuminate the general principles involved. Moreover, it offers excellent grounding for the student of mathematics, engineering, or physics who does not intend to specialize in mechanics, but wants a thorough grasp of the underlying principles.
The late Professor Lanczos (Dublin Institute of Advanced Studies) was a well-known physicist and educator who brought a superb pedagogical sense and profound grasp of the principles of mechanics to this work, now available for the first time in an inexpensive Dover paperback edition. His book will be welcomed by students, physicists, engineers, mathematicians, and anyone interested in a clear masterly exposition of this all-important discipline.
This outstanding volume, designed for junior and senior undergraduates in physics or electrical engineering, is an unusually comprehensive treatment of the subject. The book begins with the basis of electric and magnetic fields and builds up to electromagnetic theory, followed by a number of related and subsidiary topics, including relativity.
Chapter 1 gives a detailed treatment of the del operator with many examples. Chapters 2–7 cover magnetostatics and electrostatics, including Coulomb's law, electrostatic and magnetostatic curl in a vacuum, Gauss's law, electrostatic and magnetostatic divergence in a vacuum, and electrostatics and magnetostatics in matter. Chapter 8 is devoted to three special methods for solving various problems in electrostatics. Chapter 9 deals with metallic conduction, and chapter 10 is concerned with ferromagnetism. Chapter 11 discusses the basic phenomena associated with variations in time. Then chapter 12 treats electric circuits. After chapters on special relativity and the connection between electricity and magnetism, the last five chapters deal with waves of various kinds: plane waves, transmission lines, reflection and refraction, guided waves, and radiation.
In each section of each chapter, there are several worked-out examples, illustrating practical applications of the preceding theory. In addition, each section concludes with a collection of 15 to 20 problems, resulting in a total of over 900 problems in the text, conveniently grouped by subject. Answers for the odd-numbered problems are provided at the back of the book.
Professor Shadowitz (Fairleigh Dickinson University) is well known for his often novel perspective and his ability to bridge the world of the theoretical physicist and the practical electrical engineer. This well-written text, esteemed in the field for its original and interesting material, offers an excellent exhibition of his uncommon pedagogical skills.
"A large number of exercises of a broad range of difficulty make this book even more useful…a good addition to the literature on thermodynamics at the undergraduate level." — Philosophical Magazine
Although written on an introductory level, this wide-ranging text provides extensive coverage of topics of current interest in equilibrium statistical mechanics. Indeed, certain traditional topics are given somewhat condensed treatment to allow room for a survey of more recent advances.
The book is divided into four major sections. Part I deals with the principles of quantum statistical mechanics and includes discussions of energy levels, states and eigenfunctions, degeneracy and other topics. Part II examines systems composed of independent molecules or of other independent subsystems. Topics range from ideal monatomic gas and monatomic crystals to polyatomic gas and configuration of polymer molecules and rubber elasticity. An examination of systems of interacting molecules comprises the nine chapters in Part Ill, reviewing such subjects as lattice statistics, imperfect gases and dilute liquid solutions. Part IV covers quantum statistics and includes sections on Fermi-Dirac and Bose-Einstein statistics, photon gas and free-volume theories of quantum liquids.
Each chapter includes problems varying in difficulty — ranging from simple numerical exercises to small-scale "research" propositions. In addition, supplementary reading lists for each chapter invite students to pursue the subject at a more advanced level. Readers are assumed to have studied thermodynamics, calculus, elementary differential equations and elementary quantum mechanics.
Because of the flexibility of the chapter arrangements, this book especially lends itself to use in a one-or two-semester graduate course in chemistry, a one-semester senior or graduate course in physics or an introductory course in statistical mechanics.
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