Quantum Field Theory: A Modern Introduction

Rating:
Summary: A great book
Review: I found this book very good for understanding many things. I never noticed any mathematical errors, but I never read the proofs anyway:-) I think this is a great book for all the folks who have an 'easy-going' approach to mathematics.

Rating:
Summary: Expectations unrewarded
Review: 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.

Rating:
Summary: Excellent reference book but annoying for a biginner
Review: 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.

Rating:
Summary: A sloppy job
Review: 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.

Rating:
Summary: A sloppy job
Review: 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.