The Quantum Theory of Fields, Volume 1: Foundations | Steven Weinberg

The Quantum Theory of Fields, Volume 1: Foundations | Steven Weinberg | Quantum Theory of Fields

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	The Quantum Theory of Fields, Volume 1: Foundations Steven Weinberg Cambridge University Press, 2005 - 609 pages average customer review:based on 25 reviews view larger image
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highly recommended

In The Quantum Theory of Fields, Nobel Laureate Steven Weinberg combines his exceptional physical insight with his gift for clear exposition to provide a self-contained, comprehensive, and up-to-date introduction to quantum field theory. This is a two-volume work. Volume I introduces the foundations of quantum field theory. The development is fresh and logical throughout, with each step carefully motivated by what has gone before, and emphasizing the reasons why such a theory should describe nature. After a brief historical outline, the book begins anew with the principles about which we are most certain, relativity and quantum mechanics, and the properties of particles that follow from these principles. Quantum field theory emerges from this as a natural consequence. The author presents the classic calculations of quantum electrodynamics in a thoroughly modern way, showing the use of path integrals and dimensional regularization. His account of renormalization theory reflects the changes in our view of quantum field theory since the advent of effective field theories. The book's scope extends beyond quantum electrodynamics to elementary particle physics, and nuclear physics. It contains much original material, and is peppered with examples and insights drawn from the author's experience as a leader of elementary particle research. Problems are included at the end of each chapter. This work will be an invaluable reference for all physicists and mathematicians who use quantum field theory, and it is also appropriate as a textbook for graduate students in this area.

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superb book

in my opinion this should be one of the best books in qft.
Althought I've read jauch&rohrlich photons and electrons, p.ramond, itzykson, and ultimately, hatfield, Weinberg lead all of them for many heads. The features of this book are clarity, deepness, rigor, and authoritative treatment of all the topics. The discussion for a lagrangian versus hamiltonian formalism is lucid,and no finded in any other book. Group theory is applyied when is customary without cross over the physical implications. It contains a chapter devoted to scattering like no other book, wich is clear and explain concepts involved with "in" and "out" states(other of the lacks of many books of qft). Even the problems that contain are very well picked up, and solvable in most cases. I could't find any fault or mislead in what i read in this book, perhaps any skilled reader can find some. Even binding and typography are excellent, there is nothing more valuable for hardly 40$.

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Quantum Theory of Fields

This book, along with volume II, is definitely the best of all the qft books I have read. After a year-long course based on Peskin and Schroeder I was able to calculate Feynman diagrams, but I had very little understanding of quantum field theory. To see why it is that qft is so useful both in particle physics 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 three 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 it 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. This would of course require a more modern discussion along the lines of point 2)...

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. But anyone with the necessary background interested in understanding QFT will ultimately turn here.

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Brilliant

Weinberg never disappoints the serious student of theoretical physics. There is no good reason to ignore perusing his texts.
Weinberg is a master expositor and creator of modern physics.
There simply is no good reason not to purchase his volumes.

Very thorough and logical, but somewhat difficult and painful to get through

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.

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Complete discussion

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...

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reviews: page 1, 2, 3, 4, 5

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