Undergraduate Review of Nutshell Book

"I value "QFT in a Nutshell" the same way I do the Feynman lectures."

Quantum Field Theory for Undergraduates

From a review posted by a Stanford undergraduate, Philip Tanedo. He also wrote me that he and his fellow undergrads found the introductory lectures on quantum field theory I gave at a school in Africa delightful and that he has been recommending them as absolute pre-requisites for those interested in QFT.

I have often heard graduate students say that QFT is a course that one really must take twice before one really understands--once to pick up the math (without understanding the physics), and once more to pick up the physics. Zee's QFT in a Nutshell may change this conventional wisdom.

I took a QFT course taught out of Peskin and Schroder as an undergraduate immediately after an undergrad-level Quantum Mechanics course taught out of Griffiths. Zee's book helped bridge the gap between the two courses and proved to be a golden resource for insight beyond the standard texts. While Peskin and Schroder (and many of the other modern standards--Ryder, Weinberg, Kaku to some extent) are very meticulous mathematically, "QFT in a Nutshell" introduces the mathematical tools and is then meticulous about a strong physical understanding of the topic. Zee won't let you lose sight of the big picture and his expertise in teaching the subject really shows up in his ability to highlight commonly misunderstood topics and to elucidate them with beautiful, intuitive, and physical explanations.

This is not to say, however, that Zee leaves out any of the requisite mathematics. Wick contractions and rotations, gaussian integrals, the Clifford algebra of Dirac spinors... it's all there (and often explained in unique ways that clearly delimit the physics from the math)--Zee just leaves more of the details for the reader to work out (it's only then that one realizes how one uses the calculations in more traditional texts as a crutch of sorts). In this respect, Zee's book is also somewhat unique in providing solutions to selected key exercises in the back of the book--giving readers a framework to work out calculations on their own (with all the necessary tools introduced), and then check their work. Often this leads to a much better understanding of the mathematics than following a long proof in a conventional text where it's not always clear when new tricks are being used here and there to reach a solution.

At an introductory level, this type of book--with it's pedagogical (and often very funny) narrative--is priceless. Whether you use it as a way to "get your feet wet" before taking a graduate level QFT course, or as a supplement to a more "calculational" text such as Peskin, as a text in its own right, or even as a reference, the book is full of fantastic insights akin to reading the Feynman lectures. I have since used "QFT in a Nutshell" as a review for the year-long course covering all of Peskin and Schroder, and have been pleasantly surprised at how Zee is able to pre-emptively answer many of the open questions that eluded me during my course. 
In this respect, Zee's very short chapters and anecdotes make it an excellent book to read cover-to-cover. One can absorb a few sections of the book at a time as bedtime reading and be amazed at how much understanding is packed into the short expositions.

For example, in chapter I.2 (unfortunately not available through the Amazon preview at the time of this review--perhaps Google print?) Zee explains the path integral formulation using a "very Zen-like" thought experiment based on the double slit experiment. In typical fashion, Zee presents the explanation in the frame of an annoying student ("Feynman") in a quantum mechanics class who asks the professor what happens when one adds more holes to the screen of the double slit experiment... and then more screens--until you have infinite number of screens each with infinite number of holes. Later on he introduces a character, Confusio, who asks all the 'naive' (but deep!) questions that a good QFT student should be thinking about. In this way, Zee is able to teach the subject while encouraging his readers to actively interpret and understand theories rather than formulae. Along the way, Zee's anecdotes also impart a pleasantly surprising amount of "culture" --humorous stories about the early days of Feynman diagrams, quotes from old texts (one priceless quote from Bjorken and Drell expressing the "dangers" of the renormalization group was particularly funny), and a dash of historical motivation.

The latter part of Zee's text serves as an introduction to many aspects of current research--I found this especially valuable as a way to bridge my understanding from my first QFT course to being able to pick up review articles on supersymmetry. The treatment of condensed matter phenomena is also particularly important, since many modern QFT books are heavily particle-physics based.

It may sound sacrosanct, but I value "QFT in a Nutshell" the same way I do the Feynman lectures. In response to some of the other comments that Zee's book doesn't treat calculations very thoroughly, this is true--but this is *not* a negative. Zee's book isn't a recipe book for Feynman diagram calculations, it's a text to teach an understanding of physics. In the same way, one could complain that the Feynman lectures were weakened by the fact that they didn't explain very nut and bolt about how to calculate problems in freshman physics.