Tuesday, January 31, 2006

Quantum field theory textbooks

This article, originally called "QFT didactics", is a list of some quantum field theory textbooks.

Matt Schwartz: Based on his very popular introductory QFT courses, Matt's book is excellent in its balance between concentration of useful things and accessibility. It beautifully discusses connections of QFT with classical electromagnetic theory i.e. black hole radiation, and with non-relativistic quantum mechanics (and e.g. its perturbation theory), among other things. It is a very pragmatic guide not only for a phenomenologist, telling people what works – I sort of like it because I have learned from similar books a lot when I was a teenager. There are many problems in each chapter and their usefulness have been tested by Harvard graduate students. The main goal is a practically oriented one: to help the reader become a skillful practic in the Standard Model and perhaps theories extending it. A shorter free web version.

Peskin and Schroeder. This textbook has become the new mainstream standard and replaced many older books such as Bjorken-Drell.

Weinberg's three volumes. Steven Weinberg who needs no introduction wrote a more detailed set of three volumes with some interesting yet reliable things that go well beyond the mainstream material. The three volumes are Foundations, Modern Applications, and Supersymmetry.

Mark Srednicki. The textbook of the physicist who is also the chair of physics at UCSB has been available online and it has been praised by many readers. It's time for you to buy the real version.

Anthony Zee. Anthony Zee is Mark Srednicki's colleague from UCSB. His book is really cute, has a funny cover, and offers some intuitive physical concepts that are not explained elsewhere, much like some cute stories from the history of physics.

Tom Banks (2008). I recommend you a new book on quantum field theory by my (former) adviser, Tom Banks. There's a lot of wisdom – especially some conceptual wisdom – that I have learned from, too. For example, at the very beginning, he starts with a wonderful explanation why "fields" are needed to combine relativity with quantum mechanics at all – why there would be conflicts with locality (signals can't propagate superluminally) if you worked with a wave function for 1 particle (or another fixed number of particles) only. Many things are presented in a similar way as I would do, and others are done differently. A nice summary of LSZ formalism, gauge invariance and its roles, the fate of different types of symmetries, phases of gauge theories, renormalization and the logic of effective field theory, instantons, and monopoles, among other things.

Álvarez-Gaumé and Vázquez-Mozo. An invitation to QFT. You may get a similar text freely on the arXiv.

Lowell Brown. Lowell Brown's book has been praised because of its pedagogical value but be ready that its scope is limited. The author chooses a perspective in which quantum field theory is just another level of computing mechanics and quantum mechanics. That's why things like non-Abelian gauge theories are completely missing.

Renormalization methods: a guide for beginners, by W.D. McComb. It is a fun book that can explain renormalization even to undergraduates, as many reviewers argued. Renormalization is normally associated with quantum field theory - and the text covers some of it - but it first appeared in classical physics. Many examples are very intuitive and accessible.

Michio Kaku: Quantum field theory, a modern introduction. Covers quite a lot, from motivation, Noether theorems, type of scattering, gauge theories etc. to BRST quantization (only two pages), string theory, supersymmetry, and quantum gravity. Sometimes the presentation may be too short but it is helpful as reference and there are other advantages. Includes extensive problem sets.

Eberhard Zeidler. I haven't read it but among other things, this book has a very detailed coverage of history, the role of Göttingen, a presentation of heuristic methods etc. Quite original!

This list is far from complete but if someone is looking for a textbook, it could be useful. See a similar list of string theory textbooks and the 2012 explosion of stringy/SUGRA/QFT textbooks, including one new QFT textbook that looks really cleverly organized and balanced.

Many of the readers have strong opinions - and they may want to share their ideas what they think is most important for teaching QFT. In what direction would you push the classes? What do you think is missing in the mainstream courses and/or textbooks?


  1. Dear Lumo,

    this is a slightly more serious request than my usual joke comments ;-) and I'd be happy if you could give me a good advice on the following:

    I'm now looking for a QFT book from which I can really and a bit more sereiously learn how to do calculations things myself, for example in the context of applying QFT to turbulence theory.

    Unfortunately I'm not among the stellar bright wizzards who can discover or invent many tricks themself; I rather need to first "passively" follow detailed examples to see how it works before I try to do it myselfs. That is why I appreciate the Demystified books so much. The QFT Nutshell I like too, but as Tony Zee says himself, this book is rather intended to grasp the physical concepts than to learn how to calculate things.

    Dear Lumo, could you give me a hint which of these QFT books could best fit my needs, I would really appreciate it :-) ?

    (If my question is too annoying or importunate, just ignore it ;-) ...)


  2. i know that Weinberg's books are not for beginners. QFT demystified is way easier but it is not that easy.

  3. also quantum field theory in a nutshell is not for beginners.

  4. Thanks George,

    QFT Demystified was quite appropriate for me :-), and now I'm looking for something to go further from the starting point I have. From the Nutshell I quite liked the path integral approach to derive Feynman diagrams, I think I like it a tad better than the Dyson operator approach; I dont know why.

  5. Dear Dilaton, that's a great question. I think that there are many folks who would prefer a book of the kind you describe. However, I don't know the right answer. You may still want to try some of the most conventional textbooks, like Peskin Schroeder, because I am worried that all the "special spirit" books from Weinberg to Zee etc. are counterindications.

  6. i know deep down things by Bruce Schumm is easy if you have not read it

  7. Asher KirschbaumAug 9, 2013, 9:36:00 PM

    I anyone interested in quantum field theory should look into "Fields of Color: The theory that escaped Einstein" by Rodney Brooks. it is not a textbook, but it is a great introduction to quantum field theory in layman terms.

  8. @Dilaton. Maybe a little late, but I would recommend this book.


    It doesn't use the path integral approach but the canonical approach - Fourier decomposition of the field in terms of creation and anihilation operators, derivation of propagator from vacuum expectation value, derivation of Feynman diagrams from S-matrix and Wick's theorem. To understand QFT, what you really need to understand is where the Feynman diagrams come from and if you follow this book, it will explain you just that in the fist 6 chapters. After that it shows you exactly how to calculate things - decay rates and cross sections. In later chapters it deals with renormalization, gauge theories etc. The book is not easy but it is managable with patience.

    I must say that I own the Demystified QFT book also but I do not like it. IMHO it doesn't teach you the real stuff. It is all simplified to the point of being useless. It shows you the recipe how to set up an integral from a Feynman diagram, but doesn't really motivate why it is so and hence it is shallow. The path integral formulation is imho not good for a beginning. You have to compute crazy stuff like the Grassmann integrals - integrals of Grassmann numbers which are not even numbers but some crazy mathematical trick

    Another book to try might be this one


    Here are some sample chapters to check if you like the style.


  9. Oh, thanks Mephisto for these reviews and suggestions, these books look very promising :-).

    I know and agree that the Demystified books (alone) are not appropriate for getting a real deep understanding or teach one doing "real world calculations". But for topics I did not take university courses on, they gave me generally a good first impression about the topics at a slightly deeper than equation-free popular level ...