An Introduction to Group Therapy for Particle Physics

The latest CERN Courier book review section is out here. Besides a long review of Frank Close’s The Infinity Puzzle, there are some short reviews, including one for Stephen Heywood’s Symmetries and Conservation Laws in Particle Physics: An Introduction to Group Therapy for Particle Physics. That’s one I really want to see: I’m all for symmetries and conservation laws (see here), and Group Therapy for Particle Physics (at least for particle theorists) seems like an excellent idea.

This semester I’m not doing Group Therapy, but I am teaching group theory and representation theory. The class has started and I’m trying to write up lecture notes. One discouraging/encouraging thing is that looking around the web one finds several places other people have done this better, links are slowly getting added on the class web-page. The course is mainly aimed at mathematicians, hoping to provide our graduate students the background they need for several different areas, including number theory. It will however have a physics flavor, with more concentration on topics like spinors, geometric quantization, the Heisenberg algebra and oscillator representation than usual. The Dirac operator may even put in an appearance, we’ll see…

Update: Turns out there are more books on group therapy in particle physics. See here for J.F. Cornwell’s Group Therapy in Physics, Vol. 1. John Gribbin’s promotional In search of superstrings includes an appropriate appendix on Group Therapy for Beginners. Then there’s Terry Tomboulis’s Renormalization Group Therapy, which is something different.

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20 Responses to An Introduction to Group Therapy for Particle Physics

  1. theoreticalminimum says:

    Pierre Ramond’s “Group Theory: A Physicist’s Survey” is probably a book you’d like.

  2. jpd says:

    live by word completion, die by word competition

  3. Mithras says:

    I picked up the Infinity Puzzle on your recommendation; I suppose I’ll now have to pick up Heywood’s book as well.

  4. AS says:

    What’s the best opposite, say “Particle Physics for people who already know about groups and representation theory, and aren’t afraid of functors” ?

  5. ? says:

    Isn’t hosting a link to an illegal download going to get you in trouble with Columbia? The link is definitely illegal.

  6. Barry Adams says:

    I liked S. Sternberg’s, Group Theory and Physics, was on my reading list as an undergrad and its one I often return to.

  7. SteveB says:

    This is quite funny. But now I have to point out your typo in the Update. A new particle the: Renormaliz-a-ton, which is akin to the instan-ton or par-ton, I suppose.
    Sorry…couldn’t resist.

  8. Peter Woit says:


    I don’t know a good answer for that, curious if anyone else does. I’ve always intended someday to try and write something like that, basically an explicit mathematical description of the standard model, aimed at mathematicians completely familiar with the technology of differential geometry.

    Not particle physics, but some of what I’ll be doing in my class and hopefully writing notes about is basic quantum mechanics, expressed in the language of representation theory. This won’t get really to particle physics, where the interesting groups are infinite-dimensional.

  9. Peter Woit says:


    Thanks! Fixed. Typos are hard to avoid…

    The illegal download links for that turned up first, I didn’t realize that the legal sites had the same title. I’m removing that link, putting in a legitimate one.

  10. Tim van Beek says:

    AS asked:

    What’s the best opposite, say “Particle Physics for people who already know about groups and representation theory, and aren’t afraid of functors” ?

    The slightly more general question Quantum Field Theory from a mathematical point of view has been discussed both on the theoretical physics stackexchange site (see link) and on mathoverflow (the link to mathoverflow is in the second comment under the question).

    Peter wrote:

    I’ve always intended someday to try and write something like that, basically an explicit mathematical description of the standard model, aimed at mathematicians completely familiar with the technology of differential geometry.

    Don’t underestimate the amount of physics one needs to understand (Hamiltonian mechanics, classical electromagnetism, quantum mechanics, particle physics).

    IMHO there is no easy way for mathematicians to understand the standard model.
    But I would recommend to every mathematician to read the classic “Spin, Statistics and all that” (Wightman/Streater) in order to understand what a QFT is, actually, before trying to understand Lagrangian QFT heuristics.

    (And next Schottenloher: “A mathematical introduction to conformal field theory”).

  11. Chris W. says:

    I remember my first day in an undergraduate course in group theory and quantum mechanics many years ago, taught by a condensed matter physicist. A few minutes into the class, one of the students stood up (while looking quite embarrassed), collected her stuff, and quickly left the room.

    The student never came back, so I assumed at the time that she had initially misunderstood the course’s subject matter, and dropped it when she realized her mistake. My guess was that the term “group theory” had implied something else to her that she was more familiar with, but I never got a chance to confirm that.   🙂

  12. Peter Woit says:


    Thanks for the reference. Looking at the mathoverflow version

    I realize that I sent in a response there which is relevant.

    I don’t think giving a mathematician a fairly precise definition of the Standard Model in a high-level mathematical language is going to cause them to “understand” it, since there are all sorts of ideas implicitly packaged in such a definition that you really need more basic training in physics to understand. However, it might give them an entry-point to starting to learn more about the subject.

    Streater and Wightman style axiomatic QFT is quite problematic for this purpose. It is very much dependent on exploiting Minkowski space symmetry, and it really can’t handle gauge symmetry. There’s also no path integral there. If you want to try and start understanding the SM from a geometric, coordinate-invariant perspective, the path integral is a much better place to start.

  13. cormac says:

    Hi Peter, Dad has a book on group theory for particle physicists called ‘The Group Structure of Gauge Theories’ (OUP) . It gets a lot of respect though I gather it’s at quite an advanced level

  14. Andrzej Derdzinski says:

    “Geometry of the standard model of elementary particles” is a book I wrote over 20 years ago. It deals with the classical level only.

  15. It would seem that spellchecker is sometimes too much of a good thing. Once I discovered a reply on a political blog from a self proclaimed English professor that used the phrase “out of sink.” (sigh)

  16. Belastingvrije auto's says:

    Hi, J.F. Cornwell’s Group Therapy in Physics, Vol. 1 is essential imo to read for anyone interested in group theryapy & theory in physics. Although you probably have to read it more than once. 🙂

  17. Chirag says:

    Does anyone have any recommendations for an elementary discussion of phase transitions and group theory? From what I understand Morse theory is also important. I would be interested in knowing if there are any elementary survey papers on this circle of ideas.

  18. Jeff M says:


    While I have no idea what the physics reference would be for phase transitions and group theory, for Morse Theory the great reference is “Morse Theory” by John Milnor. Truly beautiful book, really thin and you will not only learn Morse theory you will get a wonderful writeup of everything you need to know about differential geometry.

  19. former mathematician says:

    Fraser’s review omits any reference to Close’s discussion of Bjorken’s work. Strange, since Close’s table-pounding about Bjorken’s contribution was the single strongest impression I got from the book.

    The only other book by Close I have read is “Neutrino,” which has similar table-pounding for Bahcall. It seems that non-recognition of theoreticians in experimental Nobels is a hobbyhorse of his.

  20. Jon says:

    @Jeff M@Chirag

    There are online copies of Milnor’s Morse Theory available here and here. Not sure if they’re completely legit, but they’re hosted on university servers.

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