Sadly, I'm not here to announce that applications are now being accepted for students who would like to participate in this year's Undergraduate Theory Institute. That's because there is no such thing as the Undergraduate Theory Institute, at least as far as I know. (Google doesn't know of one either.) But I think it would be a great idea -- maybe if I post it here on the blog someone will start it. It's increasingly common for physics students to particpate in some kind of research during their undergraduate years. The NSF has a very successful Research Experience for Undergraduates program, for example, that funds students to do summer research, typically at an institution other than their own. Getting involved in research as early as possible is a great idea for students, for a number of reasons. Most importantly, the flavor of doing real research, where the answers aren't in the back of the book, is utterly different from almost any classroom experience or even self-study, where you are trying to learn material that someone else has already mastered. The move from following a course of study to striking out into the unknown is one of the hardest transitions to make during graduate school, and getting a head start is an enormous help. On a more prosaic level, it's useful to work closely with an advisor who can end up writing letters of recommendation. And let's not forget that it can be a lot of fun! Unfortunately, the prospects are very different for students who want to do theory vs. experiment. It's often true that, on an experimental project, a student with just a hand on the basics of introductory physics can come in and learn something about the particular experiment being undertaken, and after a brief learning period can soon be contributing seriously to the work. On the theoretical side, the learning curve is much less steep, and a lot more background knowledge is required before a student can do something interesting. In my field, until you've at least taken courses in quantum field theory and general relativity, it's hard to do original work. Nevertheless, like many other theoretical physicists, I get a lot of requests from undergrads who would like to do research. I very much enjoy doing research and having students, but to be honest it's often very difficult to find things for them to do, since the background just isn't there. I've done it, quite a few times -- I've supervised four Bachelor's theses, and three summer research students. Sometimes everything falls into place, and it ends up with an interesting publishable paper. More often it's an excuse to let the students learn a bit GR or QFT, and maybe get started on the very basics of a problem, before they grow up and graduate. There's a perfectly good response to this situation, which is: even if you eventually want to become a theorist, it's a great idea to do experimental research as an undergrad. Maybe you won't be immersed in the kind of work you ultimately want to pursue, but (1) understanding something about how experiments work is an unambiguously good thing, and (2) the important lesson is not in the details of the particular field, but in what it's like to do research, which is almost independent of the type of research you're doing. That's what I did, when at Villanova I did work on photometry of eclipsing variable stars; I got a nice paper out of that. (And my favorite star, Epsilon Aurigae, will be going into eclipse again in another couple of years, at which point I expect our model to be spectacularly confirmed, and fame and fortune to follow.) And I tell this to people all the time, but still the students want to do theory! Impatient little buggers. But I can hardly blame them -- we lure them into the field with elaborate tales of black holes and supersymmetry and dark energy, and it only eventually becomes clear that they won't really learn about that stuff until they're well into grad school, if then. So I had the idea for an undergraduate theory institute. The amount of theoretical background you need to do useful work is quite substantial, much larger than one could squeeze into one summer, it's true. On the other hand, six weeks of fairly intensive study between the junior and senior year could serve to introduce enthusiastic students to many of the basic ideas they will eventually be encountering as theorists. If nothing else, they could become familiar with a bunch of buzzwords they'll be hearing for years. That sounds superficial, but could potentially be of great use -- it means that they can immediately start going to seminars and chatting with professors when they get to grad school, and have a much better grasp on the kinds of ideas that are being thrown around. So, a six-week summer course for undergrads. Much self-study, but regular lectures by faculty and perhaps postdocs. A couple of seminars on sexy stuff of current research interest, as a reward, but mostly focusing on the basic tools of theoretical research in field theory and gravitation. (Since that what I know about -- other specialties are welcome to chime in!) Here's what I imagine the syllabus to basically be like:
Special relativity, index notation, vectors, tensors.
Lagrangian and Hamiltonian mechanics.
Classical scalar field theory.
Gauge theories and electromagnetism.
Basics of Lie groups, SU(n).
Non-abelian symmetries.
Spontaneous symmetry breakdown, the Higgs mechanism.
Topological defects.
Spacetime curvature and Einstein's equation.
Schwarzschild and Robertson-Walker spacetimes.
Basics of field quantization and Feynman diagrams.
Something like that, anyway. It seems like a tremendous amount to cover, but it would all be fairly brisk, and there are benefits to be gained by seeing it all at once in the same place, surrounded by a group of other bright students studying the same material. Wouldn't you have loved to have such an introduction as an undergrad? If we put together some nice lecture notes, I'm sure it wouldn't be too hard to get them published as a cheap reference book. All I need now is a substantial (and reliable) source of funding, someone to write the lectures and deliver them, a host institution, and an organizational wizard to take care of logistics. I will look over the whole operation as a benevolent, if somewhat disconnected, father figure, whose main role will be to shoot the breeze with the students at the late-night coffee and whisky hours. Any takers?
