String Theory for Undergraduates

I hadn’t realized how many of the physics departments at the top universities in the US have instituted undergraduate string theory courses.  The only one I was aware of was MIT’s 8.251, String Theory for Undergraduates, taught by Barton Zwiebach, who developed a textbook for the course, A First Course in String Theory. 

Maybe now that there’s a textbook, that is what has caused other institutions to follow suit.  Caltech has Physics 134, String Theory, and Carnegie-Mellon has Physics 33-652, An Introduction to String Theory.  Stanford goes its competitors one better by having two undergraduate courses in string theory: Physics 153A, Introduction to String Theory I, and Physics 153B, Introduction to String Theory II. This last course even promises to explain to students how string theory is connected to particle physics. 

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119 Responses to String Theory for Undergraduates

  1. woit says:

    Thanks for the advice James, but I do think that what I am doing here and with the book that I wrote was to utilize my professional skills to the benefit of the high energy physics community.

    And both projects are parts of my professional life.

  2. Stefan says:

    To Everyone:

    This weblog seems filled with posts from individuals already committed to one view or the other on the (supposed) correctness or incorrectness of string theory. If we were discussing religion – say on the issue of how many angels can dance on the tip of a needle – “scientists” would readily dismiss us for being dogmatic-minded zealots. The ultimate anyone (at least those who do not claim to know the inner workings of nature beyond that which is currently known via experimentation) can say is… “Let us see. Maybe it will turn out ultimately be the correct formulation of fundamental physics, maybe not; but it doesn’t hurt to explore…” I think every string “hypothesist” would ultimately agree to that point. Otherwise, we lose that ultimate sense of objective understanding which has guided the scientific enterprise so fruitfully since its inception.

    To Peter:

    When is your book coming out?
    Also, (as asked in the previous post), do you know of any site / focus group on mathematical aspects of gauge theories? If not, do you want to start a group? I’m hoping this may prove valuable for the general HEP and Math-Phys communities. (At least it should to a cross-section, including string-“hypothesists” themselves.)

    Best wishes.

  3. Stefan says:

    Hi Peter (again),

    Just finished reading ‘String Theory: An Evaluation’; I encourage open-minded individuals to have a look through it; for string-enthusiasts: there probably isn’t much to change your minds.

    Some quotes (please read the article first, because these quotes can readily be misinterpreted):

    “From a mathematician’s point of view, the idea that M-theory will replace the Standard Model with something aesthetically more impressive is rather suspicious.”

    [Stefan]: Do you elaborate greatly on this point in your book? What motivated you to remark as you did?

    “To the extent that the conceptual structure of string theory is understood, the Dirac operator and gauge fields are not fundamental, but are artifacts of the low energy limit. The Standard Model is dramatically more “elegant” and “beautiful” than string theory in that its crucial concepts are among the deepest and most powerful in modern mathematics. String theorists are
    asking mathematicians to believe in the existence of some wonderful new mathematics completely unknown to them involving concepts deeper than that of a connection or a Dirac operator. This may be the case, and one must take this argument seriously when it is made by a Fields medalist, but without experimental evidence or a serious proposal for what M-theory is,
    the argument is unconvincing.”

    [Stefan]: Good remark. Where can we find useful info on Dirac operators? What about Steven Weinberg’s opinion? Does he feel similarly to you?

    “Even granting that string theory is an idea that
    deserves to be pursued, how can theorists be encouraged to try and find more promising alternatives? Here are some modest proposals, aimed at encouraging researchers to strike out in new directions:
    1. Until such time as a testable prediction (or even a consistent compelling definition) emerges from string theory, theorists should publicly acknowledge the problems theoretical particle physics is facing, and should cease and desist from activities designed to sell string theory to impressionable youths, popular science reporters and funding agencies.
    2. Senior theorists doing string theory should seriously reevaluate their research programs, consider working on less popular ideas and encourage their graduate students and post-docs to do the same.
    3. Instead of trying to hire post-docs and junior faculty working on
    the latest string theory fad, theory groups should try and identify young researchers who are working on original ideas and hire them to long enough term positions that they have a chance of making some progress.
    4. Funding agencies should stop supporting theorists who propose to continue working on the same ideas as everyone. They should also question whether it is a good idea to fund a large number of conferences and workshops on the latest string theory fad. Research funds should be targeted at providing incentives for people to try something new and ambitious, even if it may take many years of work with a sizable risk of ending up with nothing.
    Particle theorists should be exploring a wide range of alternatives to string theory, and looking for inspiration wherever it can potentially be found. The common centrality of gauge fields and the Dirac operator in the Standard Model and in mathematics is perhaps a clue that any fundamental physical model should directly incorporate them. Another powerful and unifying idea shared by physics and mathematics is that of a group representation.
    Some of the most beautiful mathematics to emerge from string theory involves the study of (projective) representations of the group of conformal transformations and of one-dimensional gauge groups (“loop groups”). This work is essentially identical with the study of two dimensional quantum field theory. The analogous questions in four dimensions are terra incognita, and
    one of many potentially promising areas particle theorists could look to for inspiration.

    [Stefan]: Why not post all the most important reference works on the above topics? This will no doubt attract more individuals looking for further ideas to work on.

    During the 1960’s and early 1970’s, quantum field theory appeared to be doomed and string theory played a leading role as a theory of the strong interactions. Could it be that just as string theory was wrong then, it is wrong now, and in much the same way: perhaps the correct quantum theory of gravity is some form of asymptotically free gauge theory? [Stefan: Important proposition] As long as the
    best young minds of the field are encouraged to ignore quantum field theory and pursue the so far fruitless search for M-theory, we may never know.”

    [Stefan]: Agreement all-round.

    Seems like we have great many things we can agree upon. 🙂


  4. MoveOnOrStayBehind says:

    >The basis for this statement is that I believe the following (somewhat vague) ingredients are necessary for being taken seriously:

    (1) Well-known high energy physics results in research papers
    (2) Presence as an invited lecturer at respected high energy physics conferences
    (3) Persuing a serious research program in high energy physics

    Well, you forgot the most important point above all: namely saying something which is reasonable and makes sense. This and nothing else counts. The statements given here and elsewhere constitute a gross misrepresentation of a well-motivated and very successful major research effort, and thus it is no surprise that they are not taken seriously by any expert, rather the only people who react are laymen who can be easily fooled by such statements. To impress experts and be taken seriously by them, takes somewhat more than what emanates from here; laymen of course cannot distinguish this from real science, and easily become victims of this private crusade.

  5. woit says:


    Sorry, but I don’t know of any specific group of the kind you ask about, and I’m afraid I’m already overwhelmed by moderating this blog, not interested in starting up another forum that would be even harder to moderate.

    I’ll try to answer some of your questions about the material in the book, don’t have time right now to really do them justice:

    1. The passage you go on to quote is an elaboration of the remark about M-theory. Not sure what I can say that would be helpful and not just repeating it.

    2. There are many, many sources of different kinds about the Dirac operator, from every advanced quantum mechanics books to a huge mathematical literature. The Dirac operator is crucial to understanding the index theorem, and there’s lots of places to read about that. One thing to do is to get ahold of Atiyah’s collected works and try reading every expository paper by him on the subject.

    3. Weinberg has not been publicly critical of string theory, although after working for a while on it, he long ago voted with his feet and left the field to do cosmology. His perspective is quite different than mine, traditionally he has been quite hostile to the use of geometry in theoretical physics.

    4. In my 2002 paper on the arXiv there are references of this kind. Unfortunately when I say little is known about these problems, I’m quite serious, there isn’t much useful literature. One good place to read about a lot of this is Jouko Mickelsson’s book “Current algebras and Groups”.

  6. woit says:


    Maybe you can explain to me why almost all string partisans (except Lubos) who attack me as incompetent hide behind anonymity?

    You’re quite right that the relevant criterion is saying something which is reasonable and makes sense, which is exactly what I’m doing. The criticisms I am making here are definitely taken seriously by many experts, some string theorists some not. Recall that Lee Smolin has written a book making much the same points I do. If you actually think something I write is incorrect, feel free to say so and we can discuss this. Just joining other string theory partisans in anonymous attacks without any scientific argument gives strong indication that you can’t actually do this.

  7. Peter Woit says:


    Publication date in the US is Sept. 8, copies should be available starting August 29.

  8. David says:

    Some recent mathematical results that I found interesting on Dirac operators can be found at the following people’s websites:
    Gerald Teschl-Math U of Vienna, Susanne Teschl- Technikum Vienna, and Fritz Gesztesy- Math U of Missouri.

  9. Stefan says:

    Thanks to both of you – Peter and David – for your generous feedback. As for the focus group – don’t worry Peter, I will search for it myself.


  10. Stefan says:

    Judging from how the field of high-energy physics is currently chugging along one gets that peculiarly unnerving feeling that HEP is nearing its (pragmatic) end. Even with all the fanfare being given to strings and other approaches there does not seem to remain much scope for futher experimental verifications in the near future. As I see it this may imply one of several predicaments:

    (a) HEP research will remain murky and unsubstantiated – for as long as we can delve out great theoretico-mathematical edifices lacking any accessible means of empirical verification; but since many of us like speculative studies this shouldn’t cause us much unnecessary discomfort;

    (b) Many researchers (as hinted above) will begin to explore and branch out into new territories – territories once considered taboo within mainstream academia… like consciouness studies (a la Penrose), philosophical speculations (of all types, shapes and flavours), and so on;

    (c) some amazing body of discovery will jostle us out of our doldrums – this will most likely come from high-energy astrophysics (or some hitherto unsuspected corner of physics); a flurry of activity will ensue… until quietude once again engulfs the frontier…

    What is my point you ask? Not much, except to point out that that once-glorious field prided and envied the world over as the “crown jewel” of fundamental science is nearing its painful and aged death…

    …so let it be… so let it be…

    I wonder what former hep scientists do for a living once they leave the field?

  11. D R Lunsford says:

    Stefan, don’t you think it is a little arrogant to claim that physics is dying? Would you have said that in 1895?

    The fault, dear Stefan, is not in our Hodge stars, but in ourselves.


  12. Walt says:

    Stefan pretty clearly said HEP, not physics as a whole.

  13. David says:

    Try molecular physics. It’s fun and there are even experiments. Some of us teach in strange departments but they let us research what we want (often anyway).

  14. Stefan says:

    I was thinking more in the line of non-linear science – which promises to open up a territory still as-yet unexplored; and which may provide us with very important insights into the “physical” world – the world that we – as physicists – claim to want a more complete and thorough understanding of. I think perhaps the most crucial and outstanding results in the coming years (with attendant Nobel prizes) will evolve from this branch (my hunch anyway; Stephen Hawking was among the first – to my knowledge – to air such a view publicly).

    [If anyone is further interested Ilya Prigogine’s fantastic work ‘Order out of Chaos’ may prove a valuable read.]

    The current approaches (in HEP-research) all seem exciting – regardless of their ultimate relevance (or lack thereof) to physics as a field; I just don’t think in the long-run younger scientists will want to wager their careers on an area (say string theory, LQG, or other theory topics with little prospects of experimental verification – atleast in the near- to middle- term) which remains so far removed from experimental verifiability… but then we are all entitled to our own views…

    If strings (and perhaps altogether current HEP research) proves less and less appealing with time, some (randomly suggested) propositions include:

    (a) studying mathematical physics – there are very many traditional problems which to-date remain unsolved, e.g. finding rigorous mathematical framework for QFT, modern approaches to classical mechanics, N-body problem, and other well-known problems;

    (b) condensed-matter physics – generally a good field to study nowadays I hear;

    (c) nonlinear science – not a bad place to devote oneself if you aspire to do some ground-breaking research;

    (d) whatever scientific problems one finds interesting and/or worthy of study… as long as it remains in the purview of “experimental science” (vs. “philosophical science”); this, in its truest spirit, has been what has kept the field so rich with activity since its initial founding, and why the term “science” is held in such high regards the world over…

    Some random thoughts from my part… hope we can make a meaningful debate out of this…


  15. Stefan:

    I like point (a) of your program. Besides, with our emphasis on “high energy” in HEP, we seem to be missing a very important part of physics, both experimentally and theoretically. There are virtually no studies of time-dependent processes. In HEP experiments, such studies are almost impossible, because everything happens very fast. On the theoretical side, QFT can tell nothing about them, because renormalized QFT lacks a well-defined finite Hamiltonian.

    The property accessible to modern experiments and theory is the S-matrix, but there is a lot of physics beyond S-matrix, and we know almost nothing about this kind of physics. To learn more, it is not necessary to go to higher and higher energies. There are quite a few fundamental things that can be learned from low-energy processes with much improved resolution (especially, time resolution) of instruments.

    For example, I am very interested to know whether interaction potentials between charged particles are retarded (i.e., Lienard-Wiechert potentials). So far, nobody has measured the retardation directly.

  16. Stefan says:


    I reference to our recent dialogue on gauge theories: I just saw the movie of Atiyah on People’s Archive: Atiyah seems to have worked on Dirac Operators during his middle-years. I’m wondering if you can give me a list of important contributions Atiyah (and collaborators, e.g. Drinfeld, Hitchin, Manin, etc.) made on this topic, and also on gauge fields / theories in general (only the most significant ones).

    I gather you will have teaching / research responsibilities, so please take your time. I’m thinking this should be useful reading; I want to start a website devoted to this area.

    Just wondering why no-one has done so already.

    Your friend,

  17. Stefan says:

    p.s. Please refer to my post on ‘Atiyah and Gell-Mann’ as well.

  18. Philosophical Phil says:

    What we need is a superhero to answer our questions……Go Sparticle!!!!!

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