Customer Reviews

Guide to Feynman Diagrams in the Many-body Problem

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This book is a counterexample to the idea that one cannot write a book on quantum field theory and keep a sense of humour. Quantum field theory of course is notoriously difficult, both in terms of its conceptual foundations and in calculating meaningful answers from its formalism. Perturbation theory has been the most succesful of the methods of calculation in quantum field theory, and the visualization of the terms of the perturbation series is greatly assisted by the use of Feynman diagrams. The author has done a great job in the elucidation of these diagrams, and readers will not only have fun reading this book but will also take away needed expertise in moving on to more advanced presentations of quantum field theory. Some readers may object to the pictorial, playful way in which the author explains some of the concepts, but he does not depart from the essential physics. Mathematicians who want to understand quantum field theory can also gain much from the reading of this book. Although not rigorous from a mathematical standpoint, the presentation will given them sorely needed intuition. Quantum field theory has resulted in an explosion of very interesting results in mathematics, particularly in the field of differential topology, and mathematicians need this kind of a presentation to assist them in the understanding of quantum field theory and how to apply it to mathematics (and the other way around). In addition, readers intending to enter the field of condensed matter physics will appreciate the clarity of the author's treatment, drawing as it does on many examples from that field. This includes a brief introduction to finite temperature quantum field theory.

The use of mnemonics, pictures, and hand-waving arguments may be frowned upon by some, but as long as their use is supported by solid science, their didactic power is formidable. Arguments by analogy, and by appeals to common-sense objects are of great utility in explaining the intricacies of a subject as abtruse as quantum field theory. The author for example uses a pin-ball game, with its many scatterings, as a tool for introducing the quantum propagator, even though paths of a (classical) pin-ball are not really meaningful in the quantum realm. Once done though, he proceeds to derive the perturbation series, and as an example computes the energy and lifetime of an electron in an impure metal.

The concept of a quasi-particle is exploited fully in this book to illustrate just how one can do calculations in quantum many-body theory. The reader will find ample discussion of Dyson's equation, the random phase approximation, phase transitions in Fermi systems, the Kondo problem, and the renormalization group in this book.

Happy reading.....(and teaching).....

It is really a very good book, and even if I agree with the definition of "pedagogical jewel" given to the quantum pinball example, I would not define this textbook an introductory one, even if a non-specialist can read it without many difficulties. I read it several years after my studies, and it represented to me a good and amusing opportunity to refresh or to learn subjects I didn't remember any more or I didn't meet in university course. And taking into account its low price, it is really worth purchasing this book.

This is indeed an excellent book. Witty and insightful, but sometimes the ease, with which you're lead through it, is in the way of stressing the really important stuff. If you are learning diagrams for the first time, and intend to do some serious research using the technique, I believe this book is just not enough: it will leave you unprepared to do much beyond the problems in the book. You might want to consult a more rigorous book, like that of Abrikosov et al., but the style may be a bit of a shock to those not used to the Russian "condensed writing". As an introduction that is less painful, and more of a textbook, I suggest Fetter and Walecka's book, though it's out of print.

I can hardly add anything to the praise given to this book by other reviewers. Though one should, undoubtedly, get acquainted with more serious books on the subject, I have to confess that I am still unaware of the book that presents the material together with the terms used in the scientific papers.

For example, I greatly admire the book by Abrikosov's et al. (AGD), and I completely agree that after reading it (and Keldysh paper) one is completely prepared to using Green's functions in serious research. But the terms like "rainbow", "bubble", "particle-particle" and "particle-hole" propagatprs, though widely used and simetimes semi-obvious, are not discussed systematically in any of the celebrated AGD, Mahan, Fetter&Walecka, Negele&Orland etc.

Thus, the Mattuck's book appear to be not only funny, useful, and explaining a lot of physics (where its value can be compared with the quantum mechanical parts of the Feynman Lectures on Physics), but it also briges a gap in terminology between the basic text and the scientific slang.

In conclusion, I deeply regret that there is no similar book on Schwingers approach to the many-body physics.

This is the best book I found about Statistical Physics at an introductory level. It is a kind of book you can read almost as a novel, with a lot of examples and very clear. It is definitely the most pedagogical book about Statistical Physics ever.

I've browsed through the customary suggested textbooks on many body physics (Abrikosov et al.,Fetter et al., Negele et al., etc) and they are written with a pedagogical intention. However, the student they had in mind was the guy who was always really good in derivations anyway. The beauty of Mattuck's book is that it reminds you where an equation has been first learned. It therefore almost reads like those old gamebooks of yesteryear, where you're constantly looking back through pages. But the flow of argument is definitely there. I'd dare say it does to many body physics what Griffith's has done to Quantum Mechanics. Good starting point before you graduate to the big boys mentioned above.

First, you do not need to know Advanced Quantum Mechanics, Quantum Field Theory or Solid State Physics to understand this book
Second, it is not a kindergarten book! You can find material on kindergarten, elementary or intermediate level on Many Body Theory in this book.
Third, all exercises are answered at the end of the book which can help to get a hand on solving problems (although there is not enough exercises on each chapter which can be regarded as a problem)
Fourth, it is a clear, to the point, easy to follow and intuitive self study book on Many Body Theory.

the formidable formal complexity of the topic is such
that any introductory help is to be warmly welcomed this has proved its worth now over several decades to theoretical physicists In my opinion it is pitched at just the right level
and I would warrmly recommend it to the next generation
G E STEDMAN
diagram tehniques in group theory and
'An orthodox understanding of the Bible with Physical science'