quantum field theory books

book review

Quantum Field Theory for the Gifted Amateur
Tom Lancaster and Stephen J. Blundell
Oxford, 2014, 485 pages

If there were a prize for the Most Unappealing Book Title of the Year, this one would be a shoo-in. The idea here is that QFT is such a beautiful theory that it deserves a wider audience than just theoretical physicists. “Gifted amateur” may be a step above “dummy,” but I suspect many readers will still be put off by it.

That's a shame, because the authors do succeed in making the math less formidable. There are no “it is obvious that”s or “proof is left as an exercise for the reader”s (well, okay, yes there are, but not very many). But anyone hoping this book will make the subject easy will be in for a disappointment. Readers still need a solid background in quantum mechanics, calculus, tensors, and relativity to get much out of this book.

The challenge the authors face is that the barrier for the rest of us is not just the math, but the connection of the math to reality. To a non-physicist, an equation is not valuable for its own sake; it's just a formula you use to calculate some numerical result. A chapter that leads from one equation to another, no matter how magnificent the result, will be not be met with appreciation, but with “so, what if anything does this fancy schmancy equation do?” Without some connection to the real world, QFT will remain incomprehensible, no matter how informal the presentation.

To that end, the authors put references to electromagnetism and other familiar classical items throughout the book. There are many solved examples, and problems at the end of each chapter, but no answers. An errata list is online, but not really needed: most of the mistakes are easy, even for an “amateur,” to spot. The other books (including Zee) also have errata lists which should be consulted before reading them.

So, what's the benefit of learning quantum field theory? Well, after reading this book, you'll be able to walk up to some girl and say things like, “Hey, baby, it is obvious that
equation from qft ”.
Chicks are really impressed by stuff like this. You'll also be able to hold forth in your local bar about exactly why particles are just excitations in fields, and the other bar patrons will thenceforth respect and admire you ... probably.

But all jokes aside, the real reason to learn QFT is that this is our culture now: complex, mathematical, and rigorous. You can spend your time watching Honey Boo Boo or you can spend it learning how the universe works. This book makes the latter choice possible for a few more of us. Thanks, guys, for helping make life more bearable.

aug 03, 2014

book review

Quantum Field Theory In a Nutshell
A. Zee
Princeton, 2003, 453 pages

Quantum field theory (QFT) is the extension of quantum mechanics in two or more dimensions, or alternatively, applied to many particles at the same time. Why is it important? QFT explains why force is transmitted by particles. It describes how particles are transmuted into each other. It's one of the greatest achievements of mankind in their attempts to understand the universe. QFT is also essential if you want to learn superstring theory.

If you're a professional physicist, you'd probably read Weinberg's The Quantum Theory of Fields. Then there's this one. The 2nd edition has a few extra sections in it. Or, if you don't like talk and would rather learn it by doing problems, there's Modern Quantum Field Theory: A Concise Introduction by Tom Banks.

The main prerequisites to understanding QFT are quantum mechanics, calculus, and special relativity. For those of us whose recollection of QM is lost in the mists of time, perhaps partially overwritten in our brain by parts of random episodes of Leave it to Beaver and lyrics from Meat Loaf's Greatest Hits, there are appendices in each chapter to help us recall the mathematical tricks. Dealing with the math is probably the biggest obstacle for most people. Without understanding the math, you cannot claim to know any physics. By explaining it conceptually as he goes along, Zee tries to make the math comprehensible to anyone who has taken college calculus and is willing to work and spend the time.

The writing style is informal, but his excessive use of shorthand frequently leads to ambiguity that hinders comprehension. His informal approach will encourage some readers and grate on others.

In this book QFT is broken up into small chunks, but the real innovation here is that Zee tells us what physicists are really thinking when they write down all those fancy equations. There are two different ways of approaching QFT. Zee uses the path integral method, with some extra tricks. Weinberg and most others use the original, “canonical” method, which is a little cleaner. Each chapter has exercises and answers in the back.

apr 20, 2013

book review

Other quantum field theory books

As with quantum mechanics, when learning quantum field theory you will always need more than one book to avoid hitting a brick wall. For example, if you have trouble with Zee's method of calculating Feynman diagrams, another book, which calculates them a different way, will come in handy. Here are some QFT books that I am familiar with. Disclaimer: I have not read any of them in their entirety.

Modern Quantum Field Theory: A Concise Introduction by Thomas Banks: As the title says, it's very concise. I will skip the proof, and merely state that it is “obvious” that this is not necessarily a good thing if you get annoyed when an author skips all the steps in a derivation and leaves them for the exercises. But it has a lot of stuff, like a detailed example of Wick's combinatorics, which Zee skims over. Banks also has a big section on renormalization and a big chapter, relatively speaking, on instantons and solitons. Banks himself recommends An Introduction to Quantum Field Theory by Peskin and Schroeder.

The Quantum Theory of Fields by Steven Weinberg: This magnificent three-volume work is distinguished by an amazingly clear writing style. One advantage of this one is that Weinberg occasionally slips up and mentions something that has something to do with an experimental result, which helps to reassure the reader that we're actually talking about something real. For example, on page 146 in Volume I there's a sentence relating one of the equations to nuclear beta decay. But in general the mathematical physics is presented on too high a level for most beginners.

An Introduction to Quantum Field Theory by George Sterman: Older books like this one often defined their variables more carefully, which is helpful for beginners. This one is generally complementary to In a Nutshell, and you can get a used copy cheap. Well, you could have, until last Friday, when I got the last one.

Student Friendly Quantum Field Theory, 2e by Robert D. Klauber: I haven't actually read this one, but it has received good reviews, and it's supposed to make the process of learning quantum field theory easier. This large-format paperback follows the principle that less is more. Its 527 8½×11 pages don't cover as much as the other books. It limits itself to QED, which is the simplest part of QFT, so you don't get the cool stuff like weak interactions. Sample chapters are here.

A Modern Introduction to Quantum Field Theory by Michele Maggiore: Maggiore is a gravitational wave physicist at Geneva, so this book is a little bit more oriented toward nuclear and particle physics. QFT, says Maggiore, is needed to calculate cross sections of particle interactions. There are also chapters on electroweak theory, gauge theories, and symmetry breaking. This is the best book for readers who not only want to learn QFT, but also want to understand what, if anything, it is good for. The print quality of this one is poor, but still readable.