Customer Reviews

The Quantum Theory of Fields, Volume 1: Foundations

5 star:		(21)
4 star:		(4)
3 star:		(0)
2 star:		(1)
1 star:		(1)

 

 

For those who are receptive to its charms, this book is simply indispensible to any high energy physicist. This book is not terribly "intuitive"(in the sense that things are derived heuristically just to the point that the result seeems plausible), nor does it take a purely mathematical standpoint, emphasizing the unbending rigour of all proofs. Instead, it offers something far, far more valuable to any physicist; namely it offers truly profound physical insight into the fundamental principles of nature. This book is so chock full of brilliant profound ideas that it seems as if Weinberg put into this book almost all of the insights he has had over the course of his long, productive, and Nobel Prize winning career. He offers a truly logical presentation of particle physics, starting from the fundamental principles of quantum mechanics (superposition principle especially) and the principle of invariance under the Poincare group modulo time and spatial inversion, as well as the principle that distant measurements do not affect each other, and derives, with a minimum of simplifying assumption, the whole, wonderful edifice of quantum field theory. This set of volumes contains almost all that we know about QFT, but somehow, magically, it is not encyclopedic; it is instead refreshingly original and, as I have said before, truly profound. Also, unlike many other QFT texts, it very clearly points out how the assumptions of the theory could be weakened, and also gives an indication of what sorts of theories come from these modified assumptions. The whole book is simply fascinating, but I found the chapter on general renormalization theory particularly enlightening, especially the section on "nonrenormlizable" theories. I learned, in a particularly clear, inspiring way, that these theories are not any more or less renormalizable than standard model theories, when all terms alowed by symmetry are included in the Lagrangian. Although these theories might seem as if they have little power of prediction (after all, there are an infinite number of parameters to the theory), but in fact Weinberg argues that the nonrenormalizalbe interactions are strongly suppressed at low momenta, so it is possible for low energies to create an effective perturbation theory, which yield in this regime astonishingly precise prediction. On the other hand, Weinberg is quick to point out that for large enough energies, this perturbation expansion simply does not make sense, and that THIS is the reason why quantum gravity based on the Einstein-Hilbert Lagrangian makes no sense for energies at the scale of unification.
Although this book is truly wonderful, I would not recommend reading it as an introduction to QFT. This book is simply too intense and profound for the uninitiated. Instead, I would recommend as a first introduction Ryder's fine text, which yields enough insights to give the reader a taste of the ideas behing QFT but not so many that the reader is overwhelmed at first, followed by Peskin-Schroeder, which gives the student all of the tools that he/she will need for almost any QFT calculation.

To put the review in perspective, My Background: I am a senior undergraduate engineering/physics student with an interest in mathematics and theoretical physics. This is my third QFT book.

Things I liked about the book:
- The book follows a very logical progression. I love how Weinberg presents a coherent argument based on simple physical principles (specifically Lorentz invariance and the cluster decomposition principle).
- Weinberg takes painstaking effort to avoid hand-waving, and is very careful to enumerate (and make plausible) his assumptions. In so doing, he avoids the sort of black-magic feeling I got when reading some less well written QFT books (see for example: Peskin and Schroeder, which makes a mockery of logical progression in an effort to teach you how to calculate as soon as possible).
- The book was very thorough, and often provided an original approach to the material. The coverage of renormalization seemed natural and coherent, and since the book is presented in a logical order (rather than a historical one) Weinberg avoids justifying renormalization as some mysterious subtraction of infinities, basing it instead on general non-perterbative methods (e.g. poles of the S-matrix, etc...)

What I didn't like about the book:
- As a result of his unwavering emphasis on logical progression, and his inclusion of a vast amount of material (almost all of which is necessary to understand in order to progress through the book), the book is somewhat painful to get through. Be prepared to re-read many of the sections a couple of times, and to make very slow progress.
- Weinberg chooses to present QFT in a very general form (i.e. abstracting it from a particular field such as particle physics or condensed matter physics). This is not necessarily a disadvantage, but I often found my interest waning after reading a few hundred pages without making any contact with phenomenology. Additionally, the excercises were similarly abstract, which makes it difficult (at least for me) to particularly care about their results. (More of a problem for self-study)
- The notation is very complete, which isn't normally a bad thing. However, the equations sometimes become very cumbersome when he includes every index, and every functional dependence regardless of how redundant they may be.
- In his coverage of path integrals, he derives things using functional determinants rather than through the more common generating functional methods. I think this hides a lot of the physical insight of the path integral approach, particularly, its equivalence to the 2nd-quantized approach, and its relation to Feynman diagrams.
- This book will drive the more mathematically inclined crazy, as the author admits, it makes very little attempt at rigour, and is very uncareful. He exchanges orders of limits willy-nilly, and often is not even clear about what sort of limiting process is taking place. There is not discussion of functional integration measures, or convergence, and there is very little justification provided for regularization methods (actually the coverage of dimensional regularization is extremely sparce, and would have been unfollowable, had I not already known it).


General Comments:
- I think that, contrary to some of the previous reviews, that the first few chapters of the book (through 6) would be a good first exposure to quantum field theory. I think the reader would have a much better understanding of the theory. However, the rest of the book is quite advanced, and would not be good for the uninitialized.
- I think that in an effort to make his coverage thorough and abstracting his discussion from phenomenology, the author sacrificed some of the readability of the book. That being said, if you're serious about learning the subject, this is a good resource.

I like this book because it explains everything from first principles to the most advanced results, and this is really the best way to master such a subject. Moreover, Weinberg managed to give full proofs of all intermediate steps using only maths available to the average physicist. I don't think it is a pedagogic text, like e.g. Peskin-Schroeder, it is too demanding at some places (however the most advanced sections that can be skipped at first reading are indicated by footnotes). Paradoxically, this can make the reader's task easier because he/she gets better equipped to tackle the difficult problems, and the systematic development does not tolerate any hiatus. The contrast is in the generality and completeness: Peskin-Schroeder discuss the representations of Lorentz group only in the context of spin 1/2. Weinberg discusses them in full generality. P-S do not explain canonical quantisation of the EM field; Weinberg explains it for any kind of field. On the other hand, the first QED process computation (Compton scattering) only appears at page 362 (page 131 in Peskin-Schroeder), and it appears as a unique example, while Peskin-Schroeder teaches you how to compute any known process. So this book is more focussed on the inner working and motivations or foundations of the theory than Peskin-Schroeder or other similar books, which have applications to particle physics in mind.

Weinberg shows not only his mastery of the subject but also his skills as a teacher. The book is easy to understand provided one has mastered relativity and quantum mechanics. It would be an excellent complement for anyone who has read Bjorken/Drell or Peskin/Schroeder. In my opinion, a true understanding of quantum field theory can only be gained if one reads Bjorken/Drell, then Peskin/Schroeder and then finally Weinberg. In his book Weinberg is sort of recombining the best of Bjorken/Drell and Peskin/Schroeder and brings understanding to a new level. It is in a sense like with having read quantum mechanics by say Messiah and then reading Landau. Reading Landau first is not a good idea, but doing it after Messiah is. The same thing applies for Weinberg but for a different reason. His insight is more sparking that way.

Let me start by stating the essentials:

1. If you are a grad student in theoretical physics or you already have your Ph.D, buy this book! If you are an amateur trying to figure out how the universe works this book will simply break your heart because you will understant none of it.

2. The book is beautifully printed by Cambridge University Press. You don't see this sort of quality often these days, when the European-style el cheapo paper back has become the norm.

3. It is an expensive book, but Amazon has some bargain re-sellers. I bought my copy at a substantial discount. It was supposedly second-hand but had obviously never even been breathed on. And it got here in two days.

4. This is a book mainly about formalism and mathematics. If you get about half-way through you will eventually reach some discussion of experimental results but this is not the emphasis here.

5. Finally, on a personal note. I am a retired theoretical physicist and about forty years ago I even wrote a paper on quantum electrodynamics. So I thought that maybe I could attempt to read this book. I know the words, Hermitian operators, Lorentz transformations, stuff like that. Yet I'm having a very hard time getting through it. After about a month of trying I'm about to give up. I can read chapters 1 and most of 2, but after that it becomes too hard for me. One problem is that it is not often explained what the point of all that complicated mathematics really is. It certainly does not give me a better understanding of the physical world although I suppose it would do that if I persevered long enough. That's why I gave it only 4 stars.

This is one of the best written physics books to ever hit the market. However, it deals with an advanced topic and its not for the faint of heart or those without the proper background. Weinberg's writing style is remarkably clear. A historical introduction (which is very enlightening) is followed by a nice chapter on relatavistic quantum mechanics. Later chapters which I found very useful include a chapter titled "Quantum Fields and Antiparticles", where he introduces the Dirac formalism, and "The Feynman Rules", which is one of the best presentations on this topic I have come across. Chapters on the Lagrangian methods and path integrals are also good. I would strongly advise the reader to thoroughly study other quantum field theory books before tackling this one.

Also recommended (to get started): "Quantum Field Theory in a Nutshell"

In this book and the others in the series, Weinberg bends over backwards to make sure every line is justified so the reader does not have to stop and puzzle over logical gaps, caveats left unmentioned, etc. Also, typically Weinberg will prove the general case of a result, instead of sticking with a simple example, or referring to the literature. It should be added that these same characteristics give the book an emphasis which isn't quite suitable for a first introduction to qft; however, any serious student will want to read the series.

A superb reference book, and one that those with some grounding in quantum field theory can learn many good things from. However, I believe students trying to learn what many consider a difficult subject will have a tough go of it. Being so brilliant, Weinberg may have trouble (not so rare in physics)teaching at the level of the students, rather than from the level of the accomplished. Nevertheless, this is a book everyone in the field should have on his/her bookshelf.

This book, along with volumes II-III, is definitely the best of all the qft books I have studied. To see why qft is so essential to particle and condensed matter physics, I believe that it is really necessary to motivate its foundations and clarify its relation to ordinary quantum mechanics, as is done in this book. Weinberg does not explain everything in complete detail, but he almost always gives enough that the interested reader can fill in the gaps. I would suggest only four things to be aware of:

1) Because of his heavy reliance on the S-matrix, his intuitive motivation is less useful for dealing with theories like QCD in which the asymptotic states do not correspond to fields in the Lagrangian.

2) The treatment of renormalization is somewhat dated, in that he still first assumes a continuum theory exists, begins to calculate and finds divergences, and then renormalizes them. He does emphasize that renormalization is present even without divergences, but the cleaner Wilsonian picture, in which the regularization is part of the definition of the theory, is introduced in an "optional" section and seldom used.

3) The discussion of Lagrangian symmetries in volume I is almost entirely classical. Anomalies and spontaneous symmetry breaking don't appear until volume II, but the careful reader will "discover" them trying to understand the cases where the arguments in volume I fail. I would have preferred to an "honest" discussion from the outset.

4) Almost no mention is made of conformal field theories. This is an essential part of many applications of quantum field theory, both in condensed matter physics and quantum gravity, and even in some particle physics models. In my opinion it deserves to be part of the standard exposition. It is also an important component of the Wilsonian definition of QFT.

That said, the introduction of and motivation for gauge invariance, infrared divergences, canonical quantization, local fields, mass/coupling renormalization, and path integration are all very transparent and insightful. The canonical quantization of electrodynamics in Coulumb gauge is a very educational exercise, and it shocks me that the representation theory material in chapter 2 is not covered in all qft books. Without it we cannot even understand why photons do not have 3 spin states! Other highlights are the CPT and Spin-Statistics theorems, and the discussion of symmetries of the S-matrix.

All of this is not to say one shouldn't use other books; P&S provides necessary tools for phenomenologists, and Zee is useful in that he will tell you all the results without really justifying them. Zee especially is good for a beginner, since you know what to look for when you try and learn things properly. (Update: two new books have appeared by Banks and Srednicki which include many of the things previously neglected in QFT books.) But anyone with the necessary background interested in understanding QFT will ultimately turn here.

I have been able to get a lot out of this book. However, it is *very* complete, and the order of the book is different than a lot of other textbooks on the subject (for example Mark Srednicki "Quantum Field Theory", which I think is a better book for a first course in QFT.). AN example is that scattering theory is covered *in detail* before acgtual construction of the free field. I'd think that the latter subject would be good to cover first.
Overall, it is very complete and a great reference to use. For someone's first course, I would recommend Srednicki; however, Srednicki references this book frequently, so...