Wednesday, April 02, 2014

Matthew Schwartz: new textbook on QFT

Matthew Schwartz – whom I knew quite well when he was a student – is an associate professor at Harvard and he has also been teaching a very popular introductory graduate course on quantum field theory.

A few months ago, he released his new 900-page-long textbook on Quantum Field Theory and the Standard Model. I have only read some portions of the book so far but I may happily recommend this book to you. With some promotion, it could become the new superior standard that could beat Peskin and Schroeder and others.

The book is composed of large pages with lots of stuff on them, large fonts in the titles, and other things. This detail makes it "user-friendly" in a way I can't exactly describe but that brings some special feelings to me. For example, I think that I have learned a lot from many similarly formatted books (practical textbooks of maths for engineers? Maybe the Feynman Lectures on Physics are also similar?) when I was a teenager. (Feynman has probably also learned much of maths and physics from similarly formatted books written for engineers.)

But this is primarily a pragmatic book about quantum field theory. While Weinberg's primary goal is to explain the deepest reasons why things are true, Matt isn't afraid of sharing lots of "accumulated wisdom" about things that really work. (For example, his discussion of renormalization contains lots of heuristic memes which is a totally appropriate approach to this difficult subject.) Physicists should ultimately know why everything they believe is (probably and approximately) right but when they are learning, the amount of new stuff may be overwhelming and they may want to learn the currently believed answers before they know their justification in detail.

At the end, the Standard Model – the practically most important quantum field theory – is the main quantum field theory that the readers are supposed to learn in a way that turns them into effective practitioners. The Standard Model – that was historically built as an extension of the very successful Quantum Electrodynamics and this is how it is treated in Matt's book as well – contains pretty much all kinds of fields (and all possible fates of gauge fields, among other things) that useful four-dimensional quantum field theories do. In this sense, the focus on the Standard Model occurs "without a loss of generality". I think that this focus is a very good idea. QFT and the Standard Model (or particle physics) are sometimes taught as "two" courses but when the former is presented using the "example" of the latter, one actually saves some time.

Feynman diagrams are among the "main tools" that a particle physicist should know. The book explains why they work, how they work, and lots of diagrams that are neatly printed are actually included.

Each chapter offers lots of exercises whose usefulness has been tested and verified by actual Harvard graduate students. It's important for a physicist to "actively calculate" and not just read other people's writings. Sometimes the exercises tell you to derive some of the equations from the main text that are omitted (although many of them are presented remarkably explicitly by the author), sometimes they are examples of more general concepts explained by the author, and sometimes they make you test the waters away from the main story line of the book.

Some QFT books and courses make QFT look like an isolated subject that is disconnected from some previous "simpler" subjects like non-relativistic quantum mechanics and classical electrodynamics. Many "alumni" of such traditional QFT courses fail to comprehend the relationships between QFT and the simpler approximate theories – and the reasons why the approximate theories are still "mostly right" within their domains of validity. I must say that Matt's book doesn't suffer from this illness at all. He wants the reader to start to think about the black-body radiation from the classical viewpoint and figure out what has to be fixed; he also reminds you of the traditional perturbative expansions in non-relativistic quantum mechanics, among other things, so that you may see that QFT is really doing analogous things and many of its conclusions precisely reduce to the analogous calculations in the non-relativistic limit.

The book has been praised by folks like Arkani-Hamed, Witten, Georgi, Peskin, Wise, and others: see the page at the top. The costumer reviews are enthusiastic, too, and the long one is particularly helpful. If you're still learning or planning to learn QFT, I recommend the book to you wholeheartedly. The book doesn't suffer from various bugs of the older book – lack of uniformity, outdated statements, and so on. Try it!


  1. Is it really good as an introduction to the subject? Or more like a book you should read after you studied some less advanced book??

  2. I am convinced that it is much more beginner-friendly and newbie-optimized than pretty much any other QFT book I know.

  3. I have bought it and the book is amazing. The only thing that is missing is a good introductory chapter on solitons and maybe a BSM chapter at the end.

  4. I’m tempted, Lubos.
    You are right in saying that you cannot learn physics by reading about it. You actually have to do calculations. The blogosphere is filled with folks who pretend to understand physics because they think there is a shortcut to doing all the work. They are wrong.

  5. Dear Lubos,

    how does this new book compare to Srednicki's QFT book?
    I don't like Peskin and Schröeder that much.

  6. Someone gave a very good review of Matt's QFT course on Quora:

    I'm sure there was also a very high rating for him on Rate My Professor, but I can't seem to find the link.

  7. Yup, a whole Chapter 14, i.e. 30+ pages, is dedicated to path integrals!

  8. You get a job yet Lubos? You need to stop theorizing/philosophizing about string theory and pay your basement rent.



  9. Personnaly I have and like :
    Lubos I would be really interested to hear your opinion about my Zee's textbook and in particular how it compares to M.Schwartz's textbook.
    For some reason that I didn't analyse, I like to buy and read such kind of books even if I have already an idea about the matter presented.
    So if you have an idea of comparison, thanks in advance.

  10. Dear Tom, could I please behave as an opportunist politician and say No comment? I can't compare two books that are good in various ways. One may be so far closer to my heart, one is probably better at happy mass producing of experts, and I don't really know either of them in any detail.

  11. The book from Schwartz is in my hands now and I can recommend it to everybody who wants to learn more about quantum field theory. I feel that the presentation and the calculations (sometimes important historical ones) are deep enough to get the essence but still accessable and the math is never distracting.I think you can really see the progress in physical understanding reflected in a text book. As one example the calculation of the Casimir force is fantastic and also fits nicely to some articles by Lubos about the infinite sum of the integers etc.

  12. Did you read any of these books Motl, you cranck!!!

  13. Had the opportunity to look inside it yesterday. Liked it a lot. Especially the parts about renormalization and effective theories. Still in my opinion it is better for a student to use it as a supplement full of insights to trusty Peskin-Shroeder.

  14. Hi Lumo,

    as Christmas is coming I have just put this QFT book into my Amazon shopping cart, and to not feel too lonely it needs a "Group-Theory for Physicists" companion ... :-)

    Do you know such a nice introductary group theory book, spiced up with cool examples of where stuff in (fundamental/theoretical) physics is used and from which I can learn how to do calculate or do things?

    Why has David McMohan not written a group-theory demystified book too? Do you have his mail adress, I whould tell him to write one, LOL ;-)