The Quantum Theory of Fields, Volume 1: Foundations

I perused my library's copy of this book when I first began to study QTF. At that early point, I found Weinberg's detailed exposition to be overwhelming. Now, after reading half of Ryder's Quantum Field Theory, a quarter of Peskin and Schroeder's An Introduction To Quantum Field Theory (Frontiers in Physics), and half of Zee's Quantum Field Theory in a Nutshell: Second Edition (In a Nutshell (Princeton)), I have bought my own copy of Weinberg and I have dived in head first. After taking a few weeks to orient myself, I now find myself entranced by Weinberg's discussion. I have genuine difficulty putting this book down!Weinberg provides an informative first chapter on the history of QTF. The second chapter on relativistic quantum theory goes well with Ryder's discussion of this topic. Chapter three is on S-matrix scattering theory. I also enjoyed Weinberg's use of the Cluster Decomposition Principle in Chapter 4 as a lead in and physical motivation for his lucid discussion of Feynman diagrams in Chapter 6.Chapter 5 deserves special mention for its a comprehensive discussion of the Spin Statistics Theorem which deals with both Fermions and Bosons in one fell swoop. The reader needs some help, however, in order to follow Weinberg's comprehensive treatment of this topic. Some useful insight can be gleaned from the pdf file of the lecture posted online by Bolvan of the University of Texas on the Spin Statistics Theorem. Essentially Weinberg is seen to express the commutators or anticommutators of fields phi(x) and phi(y) in terms of spin sums. Much insight into spin sums for spins larger than 1/2 can be extracted from Weinberg's paper Phys. Rev. 133, B1318 (1964) that is part of reference 1 cited in Chapter 5.In an Appendix of Weinberg's 1964 paper one learns that identities for hyperbolic functions are useful in determining the spin sums for different values of spin (e.g 1/2,1,3/2,etc.). Using these identities, the expression exp(-2tp.J)=cosh(2tp.J)-sinh(2tp.J) {where p is a unit vector parallel to the three momentum and J is angular momentum} can be expressed in terms of 3-momentum P and energy E (with P/m=sinh(t); E/m=cosh(t), where m is the particle mass). Before reading Weinberg's treatment, I was only familiar with spin sums for spin 1/2 Fermions (see for example Peskin and Schroeder pp.48-49).In spite of reading Weinberg's papers on the Spin Statistics Theorem, however, I felt that I was still missing a great deal of the insight needed to properly understand this important concept. Although Weinberg provides a sufficiently detailed discussion of the symmetries inherent in a massive particle, including the little group that corresponds to those symmetries, his treatment of massless particles left me confused. Luckily I found a more detailed discussion of the symmetries of massless particles in the work of Y.S. Kim and coworkers. In addition to many journal articles on the subject, including many co-authored with Wigner himself, Kim and his colleague M.E. Noz have written two books which treat this topic: Theory and Applications of the Poincaré Group (Fundamental Theories of Physics); Phase Space Picture of Quantum Mechanics: Group Theoretical Approach (World Scientific Lecture Notes in Physics). I have read the latter of these two books and have found it be extremely helpful!I should also note that there is a potential difficulty and source of confusion (as one other reviewer has already mentioned) due to Weinberg's choice of metric. Instead of g00=1; g11=g22=g33=-1, Weinberg goes with g00=-1; g11=g22=g33=1. Also, rather than describing a point in space-time as (t,x,y,z) like in most other QFT books, Weinberg orders the space-time coordinates as (x,y,z,t). Weinberg's conventions change the appearance of many of the equations, space-time matrices, and four vectors. As a result the Lorentz transformation matrices now look quite different. The dot product of the four vectors p and x changes sign using Weinberg's conventions, so that what would be exp(-p.r) in Ryder or Peskin and Schroeder becomes exp(+p.r) in Weinberg. Although I will eventually get used to Weinberg's conventions, I felt that I should post these observations as an alert to others who might consider dedicating themselves to the study of Weinberg.

I bought this book for myself for a birthday treat, and I was not disappointed. His approach is refreshing and insightful, the treatment is thorough and satisfyingly complete.I wish I had this book when I was learning the subject.. As others have said, this is not for the first year graduate student. But for the serious student who has picked up some the material already, it is a must have.

The good: The content...If you are looking for logically airtight arguments, which explains pretty much every question you could think about in QFT (Why QFT? Is Poincare symmetry and quantum mechanics enough to motivate QFT? ... the answer is no), this is it. Weinberg is extremely careful in his arguments, tries to highlight every possible loophole along the way. His approach is to consider the most general case and proceed from there.The cost is it takes quite a while before we get to practical calculations and derivation of the feynman rules (the first 100 pages or so just work with principles of symmetry and locality of interactions to force QFT as a logical necessity). Not good if you want to quickly solve some homework cross-section scattering problem, but do revisit here after a first QFT course when you have the leisure to try to answer all the why? questions you skipped at first.The bad: The typography & bindingThe typography is absolutely horrible, with expressions that have gazillion roman/latin indices, curly expressions and indices hanging off of indices. For such a classic, I wish someone took the effort to latex it properly and republish it.

I ordered this book for a QFT class I was taking, and Weinberg does a very thorough job explaining concepts clearly and succinctly. Many other books lose me by jumping around too much and assuming a lot of extraneous knowledge, but Weinberg makes few assumptions about what the reader already knows.

I like the general philosophy behind the book. The author wants to explain why QFT is the way it is.

Much clearer than any other QFT textbook I have ever read.

no quarrel with the profession as the top authority

Very Good !