The Quantum Theory of Fields, Volume 2: Modern Applications

If you want to understand QFT deeply, don't look elsewhere. Just read this (and the first volume).

Excellent book!

without peer

Very Good!

In Memoriam:Steven Weinberg (May 3, 1933 – July 23, 2021)"He continued to be an ambassador for science throughout his life." (Austin, UT News, 24 July 2021).As many have noted, it is wise to study Weinberg's volume one before attempting his second volume.As with the first volume, the second requires undivided attention. The volumes refer back and forth to one another. For instance: "it is necessary that the action should contain all possible terms allowed by the assumed symmetries of the theory (read here, page 234), then also volume one (page 506). Now, volume one asks: "Is Renormalization Necessary ?" (page 521) and refers to volume two for further details regards low-energy Pions. In volume one read: "a formula like #9.5.64 allows us to derive nonperturbative results by using topological theorems to derive information about the eigenvalues of kernels" (page 413) and this will be detailed in volume two. Wise to keep both volumes at hand. Also, keep two references handy: Hardy's Divergent Series (referenced page 294, regards Borel transformation) and MIT volumes published 1980, Encyclopedia of Mathematics (referenced page 238, regards De Rham Cohomology). Being useful, whether or not you study Steven Weinberg ! Now, Steven Weinberg words of wisdom:(1) "There is today a widespread view that interacting quantum field theories that are not asymptotically free, like quantum electrodynamics or the scalar field theory with phi-four interaction, are not mathematically consistent; fortunately, the question of whether a theory is asymptotically free for some finite range of coupling constants can be settled by perturbative calculations." (page 138).(2) "it is possible that the quarks and gluons exhibit some new kind of interaction at energy scale much larger than the scale characteristic of quantum chromodynamics." (page 153).(3) "Spontaneous symmetry breaking actually occurs only for systems that are infinitely large."(page 164).(4) "Spontaneously broken local symmetries do not lead to Goldstone Bosons." (page 172).(5) "Effective field theories provide the most convenient method for working out the consequences of symmetries and the general principles underlying quantum field theory." (page 209).(6) "As has happened earlier (dispersion relations and Feynman's diagrammatic rules) the effort to bypass quantum field theory led to valuable general results, but results that can be understood as general properties of quantum field theory." (page 252).(7) "A superconductor is simply a material in which the electromagnetic gauge invariance is spontaneously broken." (page 332).(8) " This feature of superconductivity, that a Goldstone Boson forms for an attractive potential--however weak the potential may be--is a consequence of the existence of a Fermi surface, which enhances long-range effects." (page 351).Finally, I highlight the efficacy of Steven Weinberg's approach: the methodology he embraces serves the student for many a year, that is, many a year beyond any 'required' coursework. From General Relativity to Cosmology to Quantum Mechanics and Quantum Field Theory--I have benefited enormously from his monographs (Or, stronger: I did not truly understand Quantum Field Theory until studying his work).

Before Weinberg's books, a typical graduate student in theoretical physics would study the standard textbooks (e.g. Itzykson-Zuber, Peskin-Schroeder) to pass QFT courses. When confronted with actual research problems, he would discover that all he has learned is how to do calculations in perturbation theory, that he is unfamiliar with a host of ideas and techniques that are widely used in the present-day research literature and that he has to resort to original papers and reviews to learn them.Weinberg's three-volume set drastically changed this situation, giving the most authoritative and complete presentation of QFT to appear in a textbook. Although it is not suitable for beginning graduate students, it is invaluable for covering all these topics that are typically omitted in QFT courses and for providing valuable insight missing from other textbooks.The highlight of the set is Volume 2, which includes most topics where Weinberg has made his own invaluable contributions. In his inimitable style, Weinberg guides us through the great developments in QFT from the 1960's to the 1980's, including most topics that are essential for a working knowledge of modern QFT. The presentation is crystal clear throughout and every topic is presented in as much detail as it deserves. In particular, the chapters on spontaneously broken symmetries are simply masterpieces, the treatment of anomalies is the most complete ever, while the chapter on extended objects is a thorough overview of an ever-expanding subject. This book is a must for everyone working on theoretical physics.

This book has some of the most exquisite expositions on the theoretical aspects of quantum field theory that you are ever likely to run into, i.e. Weinberg's name is literally stamped on every page for brilliance. There are topics treated here that are not likely to be found anywhere else, for instance Batalin-Vilkovisky Quantization. Weinberg's treatment of the proof of renormalizability is compact and yet very readable. And his chapter on anomalies is simply speaking the authortiative treatment. This book is a must have for anyone interested in the more theoretical aspects of Field Theory. Though I would recommed a few months with Peskin & Schroeder, and volume 1 of Weinberg to get the full flavour of Weinberg's treatment.

I have found this text extremely useful as a guide to the essentials of modern renormalization theory, as well as modern quantization techniques for Non-abelian gauge theories. The chapter on extended field configurations is nice, though it is meant as an overview and guide to the literature. What I like most about this volume is the discussion of experimental or phenomenological issues that complements many of the discussions. He has a broad base of knowledge in particle physics, as well as field theory. If you don't have volume 1, get that first.