A Guide to Feynman Diagrams in the Many-Body Problem (Dover Books on Physics & Chemistry)
Dr. Lee Carlson in the top-rated review describes this book as well as I've seen:
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).....