Customer Reviews

An Introduction to Quantum Field Theory

5 star:		(13)
4 star:		(3)
3 star:		(1)
2 star:		(0)
1 star:		(6)

 

 

I consider myself to be a good physics student, I never had trouble with self study from books, if they were any good.
This book is, in my opinion, just awful.
The exposition of subjects is with no depth, most arguments are based on "physical intuition" that maybe professors, after many years, have - most of the time you simply don't understand why the Hell X implies Y like they say.
They just slap the formulas on the page, with simply not enough justification, using all sorts of "physically obvious" or "we can expect that this will be" arguments.
No depth, no depth, no depth.
Look in L. Brown's book, you will see a beautifull construction of a theory, that's they way it should look like.

I used P&S for an intro QFT course. I learned much from the text as I found it clear and full of helpful examples. Particularly nice sections were those introducing free quantum fields, functional methods (path integrals), and non-abelian gauge theories and their quantization. In other sections, however, P&S often take many pages and indirect paths towards deriving basic results, which is particularly frustrating when one wishes to use the text for reference. The chapter introducing interacting fields seems disorganized, and the treatments of infrared and uv divergences (renormalization) seem to go on forever, with interesting or important results scattered through hundreds of pages. The discussion of the Standard Model is likewise overly verbose yet incomplete, and there is no discussion of susy. In this and other ways this text is less advanced than Ryder's, though I found its presentations clearer than Ryder's.

Overall, I found this a nice book to learn from, but horrible to return to when I try to fill in the gaps of my understanding of QFT.

This is the best book for learning and teaching quantum field theory. Although it doesn't cover philosophical or very formal aspects of QFT, it is very readable and more than sufficient to teach a year long introductory course.

This book is also excellent for self study. Unlike Weinberg which is too formal or several others that are too specialized, Peskin & Schroeder presents a nice general overview of the topic.

This is by far the worst book on QFT that I know of. There is absolutely no logic or motivation. One doesn't learn concepts or computational techniques. There are many other modern texts available which are much better. Try Weinberg or Sterman, for example.

It is always extremely difficult to review any QFT text. This is no exception. I believe that a text should be judged on whether or not it succeeds at what it attempts; in this respect, I think the book is excellent. As many other reviewers have pointed out, this is a book that gives one detailed knowledge on how to calculate S-matrix elemtents and cross-sections, etc. If one thoroughly understands what is presented in this book, one is well poised to start a fine career in practical particle calculations. The flip side of this is that it is simply impossible to cover somewhat more abstract topics as elegantly as some other, more advanced texts. On the other hand, this has its advantages, especially for those who have already been introduced to field theory. For me at least, this book forced me to think deeply about what QFT is all about and how the different results of the theory fit together, just to stay afloat. This in and of itself was far more beneficial to me than any text that spells out the author's opinions on these questions could have been, since everyone has a completely different view on what QFT is about, and reading what someone else thinks it is about does not help the student who is beginning to form his own opinions very much. Getting into the details of the book, I felt that the authors did an excellent, thought provoking job on Wilson's beautifully simple ideas on renormalization; most texts treat the renormalization group as an advanced, mysterious tool, partly because it is usually presented after the older renormalized perturbation theory approach, but here Wilson's ideas are given top priority, and strong emphasis is given on the general applicability of the renormalization group to ANY field theory, be it in condensed matter physics or particle physics.
Also, despite what other reviews have indicated, I find the derivation of the LSZ reduction formula perfectly clear. The way it is derived is in my mind completely natural, namely by convoluting the n+2 point Green's function (for 2->n scattering) with wave packets that are simulateneously well seperated and have distinct momenta. The fields decouple, forming true asymptotic states and in the end producing propagators with poles at the physical masses and residues =SQRT(Z). The remaining factor is just the S-matrix element. What could be simpler than that? Incidentally, although the proof of renormalizability for gauge theories is not explicilty given, who needs it in a first or second encounter with field theory? I feel that the vast majority of students in this field do not need a proof right away. I think that almost the same thing could be said for most of the other rigorous derivations which are skipped in this book.
Although the text does not cover nonperturbative methods in any significant depth, I feel that it would be inappropriate to do so in a text of this type; after all, not all students taking first or second semester QFT end up using these methods on a day to day basis. In summary, I think this book covers the right topics for the audience that it reaches, and covers them well, if not entirely rigorously.

I can only imagine that those reviewers who sing and dance over this book have never had a serious look at Itzykson & Zuber's text on quantum field theory, which is incomparibly clearer in its presentation, much better organized and gives fuller, deeper treatment of the subjects. P&S spend almost 100 pages describing renomalization and in the end prove nothing. It suffers from a terrible lack of foundations of QFT and their discussions often lapse into worthless gibberish. The authors simply don't demonstrate a clear understanding of the principles of the subject and have cooked up a hodge-podge of this and that. Get Streater and Wightman's book "PCT, Spin ..." for a rigorous treatment of the basics of QFT and learn the subject from I&Z.

This is a difficult book to review. That a detailed study of several textbooks is needed for a thorough introduction to QFT is a well-known maxim among students of the subject. Every QFT text excels in some areas and struggles in others, and Peskin and Schroeder's book (P&S) is no exception. P&S chooses to emphasize performing calculations in the Standard Model (SM), and the chapters pertaining to this topic are excellent. Chapters 5 and 6, covering tree and one-loop calculations in QED, are invaluable, as are chapters 20 and 21, which detail the electroweak theory.

Several of the formal aspects of QFT are shunted in P&S, as must something be neglected in every QFT text that is stable against gravitational collapse. The general representation theory of the Lorentz group is the most glaring omission in P&S. Chapter 1 of Ramond's "Field Theory: A Modern Primer" treats this topic quite well. The LSZ reduction formulae are derived and discussed more clearly in Pokorski's "Gauge Field Theories", as are BRST symmetry and free field theory. For those interested in undertaking detailed phenomenological studies of the SM or some extension thereof, Vernon Barger's "Collider Physics" is also recommended.

Despite its shortcomings, P&S remains the best QFT reference currently available. It's the book I turn to first when confronted in research papers with field theoretic puzzle that I just can't crack. If you buy only one QFT text, buy P&S.

I have used this book for the past five years, teaching a one
semester course on Intro to Quantum Field Theory.
I also taught the second half of the book two times.
I am still amazed by how well written and enlightening this book
is, and I regard it as a modern classic. After a years
worth of study, the student is really able to dive into research.
They know the Standard Model in enough detail to
perform radiative corrections in the electroweak model, and
where the Feynman rules come from in different gauges.
The book is accessible to experimental and theoretical students
in all areas of physics, and drives home all the essential
points. I wish this book had been around twenty years ago
when I was first trying to learn the material.

The authors give an excellent overview of the physical concepts and computational aspects of quantum field theory. They stress the situation behind the subject, and endeavor to remain as concrete as possible. Abstract mathematical constructions are left to more advanced texts in quantum field theory. The authors characterize their book as an updating of the two volume set of Bjorken and Drell.

The main emphasis of the book is on quantum electrodynamics (QED), the most successful of quantum field theories. The representation and analysis of the physical processes of QED is done via Feynman diagrams, with electron-positron annihilation leading off the discussion. Recognizing that the exact expression for the amplitude of this process is not known, perturbation theory is used to give an approximate representation for it via an infinite series with each term involving successively higher powers of the strength of the coupling between the electrons and photons (i.e. the charge). Each term is represented as a Feynman diagram. This is followed by a discussion of the quantum field theory of the Klein-Gordon field. The authors give one of the best explanations in the literature of why one must deal with the quantization of fields and not particles, the most important one being causality. Canoncial quantization is employed and the Feynman propagator for the Klein-Gordon field is derived. The Dirac field is also quantized using the canonical formalism. The authors show that Klein-Gordon fields obey Bose-Einstein statistics and Dirac fields obey Fermi-Dirac statistics. The all-important Wick's theorem is proven and higher-order Feynman diagrams are discussed. Most importantly, the authors show how to connect these results to experiment via the calculation of cross sections and decay rates. This entails the computation of the S-matrix elements from Feynman diagrams. The authors are very detailed in their elucication of the discussion, and those who have done these calculations know that it is great fun to do so. In addition, these "bread-and-butter" calculations give quantum field theory its ultimate justification in the modern particle accelerator. The discussion on radiative corrections is especially well-written, particularly the section on infrared divergences.

The authors do not entirely neglect the more formal aspects behind quantum field theory, and spend some time discussion renormalization and the amazing Ward-Takahashi identity. This important identity gives one further confidence in the consistency of QED in that is shows that timelike and longitudinal photons can be neglected in the actual calculations. The process of renormalization has been viewed with suspicion by mathematicians, but it has been given a firmer foundation recently using, interestingly, mostly 19th century mathematics. The authors discuss functional methods, and give an example of its use by calculating the photon propagotor. Viewing this as a constrained problem because of gauge invariance they use the Faddeev-Popov gauge fixing condition to obtain the correct results. In addition, they derive the important Schwinger-Dyson equations for QED using functional methods.

Effective field theories are also introduced in the book, with an explicit calculation of the effective action. The authors show the important connection between continuous symmetries and the existence of massless particles (Goldstone's theorem). Their discussion of the renormalization group is very understandable, and they motivate the subject well, by asking why the loop integrals over virtual-particle momenta are always dominated by values on the order of the finite external momenta.

Non-Abelian gauge theories are given a thorough treatment and Wilson loops are introduced as a comparator between gauge transformations at different spacetime points. The quantization of these theories is again done by viewing the quantization problem as a constrained problem, and the famous "Lagrange multlipiers", the Faddeev-Popov ghosts, are introduced. The authors show in detail how their introduction allows the correct Feynman rules to be produced, by showing that the unphysical timelike and longitudinal polarization states of the gauge bosons are cancelled by these fields. The BRST symmetry is discussed as a formal device to to this cancellation. The omit though how the Ward identities are derived from BRST symmetry.

The authors give the best explanation in the literature of asymptotic freedom by showing the effect of vacuum fluctuations on the Coulomb field of a SU(2) gauge theory.

The important operator product expansion is treated in the context of the Callan-Symanzik equation in quantum chromodynamics. It is applied to the deep inelastic scattering and electron-positron annihilation. Dispersion relations make their appearance here.

The authors also discuss anomalies and motivate the subject by analyzing the axial current in two-dimensional massless QED. The axial current is shown not to be conserved in the presence of an electromagnetic field, and they conclude that gauge invariance and conservation of axial currents in this theory cannot both be simultaneously satisfied. This is generalized to axial currents in four dimensions and the authors derive the famous Adler-Bell-Jackiw anomalies. The implications of anomalies for gauge theories are discussed along with observable consequencies.

The (mysterious) Higgs mechanism is also discussed and compared to the situation in superconductivity. To view it in terms of superconductivity I think gives it the most plausible and intuitive justification. Understanding the Higgs mechanism is a usual stumbling-block for newcomers to gauge theories, and the authors do a fair job here. The quantization of spontaneously broken gauge theories is then carried out, with emphasis on the Goldstone boson equivalence theorem. A brief discussion of the future of quantum field theory ends the book.

When reading this book, and others on quantum field theory, I am always amazed at the degree to which it works, and its elegance, despite the fact that it really is a collection of ad hoc strategies and sophisticated guesswork. One gets the impression that there is something profound behind the scenes, still waiting to be discovered, and which will be able to shed light on the major unsolved problem of quantum field theory: the existence of a bound state.

I used this book for a year long quantum field theory course at Berkeley and feel that I learned a respectable amount from it. However, as the other reviews state, the book spends alot of time elucidating the details of the calculations in field theory while sacrificing pedagogical aspects. The little bit on representations of the Lorentz group is hardly enough to be satisfying. When I first went through this I was really wondering where in the world spinors came from (go to Pokorski's field theory text for this). Nonetheless, QED is done in a satisfying way, showing all the important calculations whose results are used throughout the text in the QCD and electroweak sections. Many sections of the book are not self contained at all. I wanted to learn about anomalies early on and found that the anomalies chapter could only be read after a thorough reading of all the QCD chapter (which is particularly phenomenological). The renormalization chapters are quite good, but it lacks a big-picture summary of how to go from measurable quantities to things like running coupling constants.
P&S do a good job of writing a very phenomenologically oriented field theory text. There are practically as many connections to experiment as you would find in a decent particle physics book. The formal structure of quantum field theory is not explored at all. Chapter 7 holds many formal results which are important for the rest of the book, however the chapter is particularly confusing. Functional integrals are explained but are not taken as the foundation upon which the QFT stands. I found the formal structure of QFT to be very well explained in Pokorski's text. In the end, Peskin is a pretty good book with which to start learning QFT. I have yet to find an introductory QFT text that I really like (I haven't checked out the Brown book). Peskin left me feeling like I knew how to do particle physics calculations correctly but I didn't really get a feel for how QFT as a logical framework fit together. After reading Peskin, one is comfortable enough with calculating in QFT to a degree that more sophisticated texts (Pokorski, Weinberg) are very accessible.