Customer Reviews

Quantum Field Theory: A Modern Introduction

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

 

 

This is a good book. The nicest thing is how it handles renormalisation, a very complete approach. However, it have severe defects in mathematics. For example, its proof of Noether theorem is wrong. It is too sketchy with group theory, although it at first sight looks like an introduction. Only someone very well versed with group theory and representation can understand this chapter. Unfortunately, this is the mark of a rather sloppy mathematics writer, as further reading confirms. The comparison with Weinberg's precision and rigor is striking. I would recommend it however to someone wishing a clear introduction to renormalisation and the standard model, but with previous knowledge of QFT. I think the term "introduction" in the title is a bit misleading.

The scope of the book is very wide, it covers many topics (even quite advanced ones) not to be found in similar books. The problem is the large number of mathematical errors and typos, and its dishomogeneity: while some topics are well covered from basics up, others really require much advance knowledge.

The Good: Nearly all the major subjects are covered in some detail - that is the key developments and insights. This includes all the major details of QED, Gauge Theory and Electroweak Theory, and finally the Standard Model. I loved the reviews on GUT, Quantum Gravity and Superstrings and a few bonus section/chapters like Solitons and Latice theories. Another good thing is the space given in the book - being a notes person, there is plenty of room to work out details and write notes beween equations and at the bottom of the page. Teh appendices contain all the necessary formulas for trace calculations but when it comes to QFT, appendices SHOULD also contain the Feynman rules for the various theories and/or interactions.
The Bad: The author has an unpleasant habbit of plugging and sticking formulas and equations here and there within developments thinking we remember exactly where it was discussed beforehand. Sorry but it becomes painfully annoying at times to understand the material presented in detail when you keep being distracted by finding the formulas 4 chapters before. If ever their is a second edition, I think many would realy like it to include more of the "Using eq. (3.113) and the normalization condition (3.etc.) we get..." more often such that we could worry less about finding which formula/equation (and where they are!) as opposed to working out the developments for ourselves - unless it is recommended as an exercice. For those that love developments and the origin of equations, Lahiri and Pal is much better. And why do textbooks of this caliber DO NOT contain worked out excercises or answers? I have done some of the exercises BUT what is the point of doing more of them if I do not know if I have the right answer! I guess I would more fully understand the material better IF I had a result like I have in the text. Learning QFT is also allowing the student to develop tool to calculate - hence worked out problems help in that endeavor.
The Ugly: I've seen better Dirac equation formulations and Wick's theorem developements (and application to second order interactions in phi4) is awful compared to other texts and not as straightforward as suggested.
In all, excellent reference book for the intermediate learner or expert that wants to avoid working out details and wants more the results and interpretation but for a student or someone who seeks to make calculations and basic research later on, Peskin and Schroeder is a better choice.

The only thing that could possibly justify the word "modern" in the title of this book is that, at the very end, it includes a discussion of supergravity and string theory. Apart from that, both the choice of topics and their treatment are fairly standard. The book is not an "introduction" either; it touches upon quite involved issues in a rather casual way. At the same time, it is sloppy both in its presentation and its notation, and some of the "proofs" leave much to be desired. It reads like something that was written in a hurry, at the expense of clarity and coherence. If one is looking for an introduction, there are far better books around. More advanced readers will be able to find books that cover the same material in a much better way, in the same number of pages.

My background is a Ph.D. (1963) in physics. My dissertation was based on the Mössbauer Effect, and my brief career in research was in areas of electron transport physics. I never had a strong background in high energy physics, and my quantum field theory exposure was mainly QED.

Now that I am retired, I read some physics and looked to Prof. Kaku's book for a survey of current QFT and an introduction to string theory. I have just finished reading Chapter 2, which the Preface states may be skipped by the student who "already understands the basics of group theory . . . or who does not want to delve that deeply into the intricacies of quantum field theory." I certainly did not place myself in that class of student and decided to delve.

The presentation of Chapter 2 leads to the "essential point" (p58) that the Lorentz and Poincaré groups are at the heart of quantum field theory, and "the results of this chapter will be used throughout the book". For that reason, the results should have been developed with great clarity, and I cannot say I found that true.

For example, equations 2.104 which state the Poincaré algebra, as described as showing that translations transform as a vector under the Lorentz group. But the transformation of a vector is defined by eq. 2.91. No connection is anywhere demonsrated between eq. 2.91 and 2.104; nor elsewhere between commutation relations and the transformation of vector fields.

In the discussion of the Casimir operator, the Pauli-Lubanski tensor (p.55), the evaluation in the rest-frame of the space part of the vector (tensor) based on eq. 2.106 leads to "the rotation matrix in three dimensions." But eq. 2.106 is an operator equation, whereas the result (eq. 2.108) is a matrix equation. What is the connection?

I shall plow on with the text in the hope that it will become clearer as I proceed. My feeling at this point is frustration, because I cannot tell for whom this book was written.

Several of the other reviewers may be correct, about the quality of the text, and the developments of some of its arguments. It does however go beyond such earlier standard texts, like Sakurai's "Advanced Quantum Mechanics", which was just an introductory treatment of relativistic quantum mechanics. Kaku takes you well into the depths of QCD and the [current] Standard Model.

If you are a grad student wanting expertise in this field, an attraction of the book is its extensive problem sets for each chapter. Perhaps more so than the textual exposition! Another reviewer bemoaned the lack of worked out problems or answers. Well, that lack is the norm for many advanced texts. You just have to get used to it. But a more positive way to look at this is to recognise that sometimes knowing that an answer to a problem exists can be valuable in itself.

In my opinion this book is just ok. The breadth of material it covers is good. You can find topics such as critical phenomena and lattice gauge theory among its twenty plus chapters. However, I don't think there is generally much depth. To me the book reads like a catalog of results, I don't see it providing students with any real mathematical or physical insights. The main use I see for it is as a reference.

Page counting isn't a perfect means to determine completeness, but hopefully it does give an impression of the style. A couple of brief examples would be BRST quantization being covered in two pages (almost all equations) and SU(5) in one page. These are just a couple of places where I thought the treatment was so superficial I wondered why it was included at all.

A more detailed example would be the treatment of quantum gravity. It goes from the equivalence principle to Christoffel symbols in five pages, the Robertson-Walker solution is covered in barely more than a page and inflation in two pages. Maybe it's me, but I just don't see people that don't already know this stuff learning it here. Another comment on this chapter concerns the approach to developing classical general relativity. It is based on the properties of covariant vectors and contravariant vectors under coordinate transformation, this is definitely not a modern approach.

The topics it covers are quite interesting, a student with an excellent instructor may find it a useful book. However, I find it hard to imagine many people learning quantum field theory by reading this book. Just off the top of my head I can think of four books that I think most people would find much more helpful in learning quantum field theory: Peskin and Schroeder, Ryder, Weinberg and Zee ("quantum field theory in a nutshell" this isn't so much a traditional text book, but it is very insightful).

Some of these reviewers need to review the title of the book. This is a "modern introduction to quantum field theory", not some in-depth study with hearty breadth. Duh. For physicist's you people don't have much common sense to speak of.

This is all around a pretty mediocre, uninspired exposition of quantum field theory. More recent works by Weinberg and Peskin & Schroder, for example, are far more coherent and elegant.

This book is an excellent reference for any student or professional in quantum theory. Although I found it very interesting, I feel that the chapter on strings should have been omitted. This could have allowed for additional mathematical proof of path integrals (Perhaps a simple axiomatic proof) or more applications of superspace to point particle theories.