Customer Reviews

Quantum Field Theory in a Nutshell

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2 star:		(1)
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This Quantum Field Theory text stands apart from others in so many ways that it's difficult to list them all :-). A very unique QFT introductory text.

One problem with learning QFT is that it is so easy to get lost in the mathematical details that the core physics concepts often get obscured.

In my opinion, Tony Zee overcomes this particular problem quite successfully. He keeps algebra to a bare minimum, and tries to find the shortest route to the physics ideas. He chooses examples that illustrate concepts in the fastest possible way.

The chapters are short. So refreshing! Each chapter has one or two core ideas. You can go through one in ten minutes (glossing over the math), and then you go back and do the math.

Part I (first eighty or so pages) is called "Motivation and Foundation" and is a rapid introduction to QFT. It is also a summary and sweeping overview --- introducing path integrals and Feynman diagrams and making a very intuitive transition from Quantum mechanics to Field theory.

The next three parts cover spin-1/2 particles (Dirac spinors), renormalization, and symmetry (breaking), standard fare for QFT texts. A sampling of condensed-matter applications is given in Parts V & VI, and then current high-energy topics are treated in parts VII & VIII.

The applications make this text stand out. There is a selection of advanced current topics like the quantum hall physics, surface growth, string theory, D-branes and quantum gravity, not usually found in introductory field theory texts. Of course none of these topics can be done justice in a book at this level, but getting a taste of advanced issues is a great treat.

The exposition is breezy and chatty, as the author admits was his intention. The text is never boring to read, and is at times very, very funny. Puns and jokes abound, as do anecdotes involving the inventors of QFT.

Renormalization is discussed through a lively dialog between student Confusio, a female Smart Experimentalist (SE), and a senior (Egghead) theorist. Ode to Galileo! Section headings alternate between serious and hilarious --- one section is called "Wisdom of the son-in-law". The path integral formulation of quantum mechanics comes out of a conversation between a teacher and a "wise-guy" student, who happens to be Feynman.

And so on and so forth.

The net result is a book which is much easier, and more fun, to read than any of the other common QFT books out there. Tony Zee's skills as a popular physics writer have been used to excellent effect in writing this textbook.

One more distinctive feature is that there is equal emphasis on condensed-matter and high-energy applications. Most QFT texts today, unfortunately, are so biased toward particle-physics that they tend to put off condensed-matter students. A. Zee has broken the mold!

Is the treatment "over"-simplified? Maybe simplified, but not dumbed-down. The high concept-to-pain ratio certainly seems worth the simplification.

Is this text only good as a supplement? Well, it is after all a "Nutshell", so maybe other texts are better for details. But as an introduction to QFT concepts, few other books match this.

Wholeheartedly recommended.

From my experiences in quantum field theory: The kind that you can read, the kind that work out examples, and the kind that your professors want you to understand. The last are Jackson-esque tomes like Peskin and Schroeder that dummies like me in a QFT class will never be able to use ("dummies in a QFT class" may sound like an oxymoron, but we're not all geniuses...). The kind of texts that works out examples, like the text by Lahiri and Pal, have been invaluable to me, but I still have not always been able to understand the IDEAS contained in the mathematics.

"QFT in a Nutshell" heralds the introduction of a book on quantum field theory that you can sit down and read. My professor's lectures made much more sense as I followed along in this book, because concepts were actually EXPLAINED, not just worked out. I still recommend having all three types of texts, but I am glad that now I have three types and not just the last two.

However, it might make sense to incorporate some of the explicit problem solving in Lahiri and Pal into "QFT in a Nutshell"; while I could understand the English, the math solutions often were difficult to follow. Just a thought.

I have often heard graduate students say that QFT is a course that one must really take twice to understand properly--once to pick up the math, and then once again 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 hints and 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.

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 holds to the screen of the double slit experiment... and then more screens--until you have infinite screens each with infinite 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 digrams, 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. While Zee's first four chapters present the core of a particle-oriented QFT course, the following chapters contain brief and readable introductions to more specific topics. 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. Later on, I've found Zee an excellent resource to answer typical 'beginning grad student questions' such as: What is a soliton/instanton, how does grand unification work, what do I know about gravitons? Sure, there are only a few pages dedicated to each of these topics, but those pages provide the heuristic insight that is an invaluable guide/motivator through more technical review literature. If you want to learn the nitty gritty about solitons and instantons, then go read a book on solitons and instantons. If you want to know what the heck a soliton/instanton is and why the heck you should spend hours reading about them, and, on top of that, you're a grad student so you don't have any time to read more than a few pages right now, then Zee's a great place to get the main idea and (more importantly) place it in context.

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 recipie 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.

So, a nutshell: You'll want to get a copy of Zee because it's excellent (if not indispensable) when you're beginning to learn QFT. You'll want to keep Zee because his later chapters will continue to shed light on the path beyond the standard QFT course. (And you'll want to keep fishing for more jokes and anecdotes.)

The first sentence of the text sets the tone: "Quantum field theory arose out of our need to describe the ephemeral nature of life." (The entire first chapter is available at http://pup.princeton.edu/chapters/s7573.pdf) This is *not* your father's quantum field theory text. I particularly appreciate that things are motivated physically before their mathematical articulation. Further, the author is willing to fill in steps (in chapter appendices), rather than take the "it will be recalled" or "it can be shown" approach across intermediate steps. Most especially though, the author's "heuristic" descriptions are the best I have read anywhere. From them alone the essential ideas become crystal clear. If you are comfortable with non-relativistic quantum mechanics and special relativity, but not so with their union, I think you will find this book very helpful.

I am really pleased that Zee undertook to write this book. QFT can be a hefty topic. All too often, writers of many texts know their topic well but do an inadequate job of conveying to the reader where they are leading them as well as identifying the important insights that can be gleaned. In this manner, Zee's book stands out from the crowd. He likes to explain how to reason through a problem or idea. As I started reading the text, I found many things started making a lot more sense to me.

From my perspective, Zee's book serves a dual role:
1) Its a great book for picking up lots of useful concepts and techniques.
2) Now that I have some orientation and sense of direction, I can go back to some of other texts on QFT and Superstring Theory and begin prying open some of the less accessible topics.

The technical community is in need of more books like this. I hope Zee will go on to publish additional textbooks on related topics (for both an introductory level, and separately on a more advanced level).

You should be aware that this book has three prerequisites: reasonable knowledge of Quantum Mechanics, Relativity Theory and a certain level of mathematical maturity. Without these prerequisites, you won't get very far in this book and will need to supplement it; whether having some other texts handy, or enlisting the help of a fellow colleague or professor to fill in the gaps.

All in all, QFT in a Nutshell is a wonderful find. For the money and time spent putting my nose to the grindstone to learn something new and useful, this book has truly turned out to be one of my better purchases.

If you want to try to understand QFT with any depth, especially if you are learning it without the aid of a teacher, this book will utterly frustrate you. I'm speaking mostly about the very first chapter, where Zee races through the fundamentals. I first started reading this book about a year ago, and since then I've read a number of other QFT texts, including Weinberg's text, which I highly recommend (though it can be more difficult).

Zee gives a good introduction to path integrals in terms of ordinary QM, but in extending it to QFT he simply tells us that we take the initial and final states to be the vacuum over an infinite time interval. All physical intuition in terms of transition amplitudes between states is lost here for a new student. Why are vacuum transitions so important? From other texts, I see now it's because the perturbation series gives us the off-shell amplitudes. But Zee never even mentions the S-matrix (which is the whole point of Feynman diagrams)! He simply says that factors of sources 'correspond to' the creation or annihlation of a particle, and so we should identify terms in the expansion of the integral with scattering processes. If you want understand where this partice interpretation comes from, you'll be very confused.

And in terms of physical intuition, this book can get very misleading. After showing how to find the propagator, he says that this represents a particle traveling from x to y (again we don't get a good explanation). And showing that the propagator is nonzero over spacelike distances, he implies that quantum particles can get outside the lightcone. He says that Feynman diagrams represent the actual spacetime history of particles, and he treats virtual particles like objectively real things throughout. Also, when first reading this book I didn't get a clear idea of the role of the fields in QFT. Are they observables? Zee treats the field like it represents the complete state of the sysem, and particles are just disturbances in the field. But if you flesh this interpretation out in terms of Hilbert spaces etc. you'll get contradictions.

If you just let yourself be guided by Zee, I'm sure you won't be too troubled, and this book does present some very interesting material, even in the first chapter. But the text overall felt sloppy. For instance, he sticks a section on nonrelativistic field theories in the middle of the chapter on renormalization, with no continuity, so when you get to the condensed matter sections much later you have to page back to this isolated chapter.

If you want to be led around to lots of new material, and correct your understanding of it later, this may be a good book. Also if you already have a good grasp of the fundamentals of QFT (or have a good teacher), and want a brief introduction to lots of material, this book may be worthwhile. But if you are just learning QFT, and want to understand how it follows from the physics you already know, do not buy this book.

This book certainly offers some insights into QFT difficult to find elsewhere. Most particularly I appreciated Zee's discussion on the relationship between the propagator of the field and the force exerted by the field. He makes frequent appeals to dimensional analysis, treats gravity throughout and includes chapters relating to statistical mechanics. It is a thoroughly modern text. Zee's purpose in writing this book was to present the conceptual aspects of QFT with as little mathematics as possible. As such he does a commendable job giving the reader an intuition for the subject that specialists in the field undoubtably take years to develop. The most stiking impression I had reading this book is that the author must be very experienced in teaching QFT as his pedagogy appears very refined.

Now I must add some personal opinions of what I think could have been improved. First there is an irony in teaching any subject that is mathematics based. By downplaying the mathematics the concept may in fact become more obscured than clarified. Sometimes a rigorous mathematical approach is THE way to illuminate the material and without it the careful student is left with an uneasy feeling of being able to explain the material to a layperson but lacking a mastery of it himself. Second, the section on renormalization is too brief. The reader will have to confer with other texts.

In conclusion this book is a taste of quantum field theory only. It is a first step to be followed by more detailed and rigorous works. In fact I believe it serves best as a suppliment to a more traditional approach.

Finally, an understandable book on QFT for average folks. Prof. Zee develops the subject using Feynman's propagator approach, which to me is the most aesthetic and intuitive way to crack this otherwise impenetrable nutshell. After the first 60 pages or so you should have a pretty firm grasp on the mathematics and the underlying physical concepts. However, having armed the reader with the bare minimum of mathematical and physical tools, Zee then dives into some fairly daunting territory without providing the requisite aids. His treatment of Grassman algebra is minimal (which is too bad, because it underlies fermionic QFT), and his explanation of renormalization is altogether inadequate. Zee then ventures into more advanced areas which, in my opinion, are clearly beyond the scope of the book's "nutshell" approach (this is the primary reason why the text exceeds 500 pages). In spite of these shortcomings, however, Zee's book fully succeeds in its aim to explain a complicated topic to those of us who learned ordinary quantum mechanics without too much difficulty, but then got slammed into a wall when we turned to QFT. My recommendation to beginners would be to read this book and then get Lewis H. Ryder's QFT book to further cement your understanding of what is undoubtedly a profoundly beautiful, if difficult, subject.

I have used "Quantum Field Theory in a Nutshell" twice now, as the primary text for a semester-long course in quantum field theory for our second year graduate students in physics. I am immensely pleased with the book, and recommend it highly for anyone who wants to reach an audience of students who would pursue thesis topics spread across the spectrum of modern physics research.

Firstly, Zee starts of with the path integral formulation of quantum mechanics, and shows that quantum field theory follows seamlessly, in fact naturally. Taking his advice early on, regarding exercising the straightforward math surrounding gaussian integrals and (what become) Wick contractions, students gain a great deal of confidence that they can understand the ambitious goals of modern field theory.

Secondly, the book gets into "real physics" quite early on. Watch how scalar particle exchange binds two sources, and appreciate Yukawa's Nobel Prize research. See that vector exchange repels two sources, and that tensors will once again attract. Get an appreciation for extra dimensions, as Zee keeps the spatial dimension arbitrary so that he can make key points. All this in the first part of the book, before needing to introduce the Dirac field.

The book need not be followed in order by chapter. After having taught out of it once, I was more bold the second time and skipped a few things and reversed the order of a few topics. I came to appreciate the flexibility of Zee's approach, and would argue that instructors better than me can make much further use of it. There are many advanced topics interspersed into the flow, such as an appreciation for Dirac spinors based on the Lorentz group, which can be incorporated into a very high power course, or skipped by more timid instructors like myself.

Furthermore, Zee provides very many "jumping off" points for further investigation of key physics topics. In my class, I followed the book to cover the Goldberger Treiman relation in particle physics, superfluidity, and critical phenomena through the Landau-Ginzburg mechanism. And, I was only able to touch on a few of the many possible topics he offers for discussion.

The book has a number of useful anecdotes which the students found at least amusing, but frequently useful for their own appreciation. It is fun to read.

I recommend the book highly. Don't let the "damn the torpedoes, full steam ahead" approach scare you off. Once you get used to seeing the physics quickly, I think you will find the experience very satisfying intellectually.

I could not imagine that one can
explain so much field theory concept in 500 pages.
I taught QFT during the fall of
2002, I regret that I did not have Professor Zee's book.