Those Little Challenges We Face

Just got back from teaching my Physics 678 class. I can't really tell you the title, since I don't really know it myself. How so?, you ask....Well, what happened is this: The semester started, and I showed up to teach what I thought was supposed to be the second part of a graduate string theory class, as long promised. (The bit where I do my standard dog-and-pony show about D-branes, etc, now that they know about basic perturbative string theory from my colleague Nick Warner's class last year. Sort of an extended version of courses I've given at Summer Schools at several places around the planet.) The first warning sign was that I looked on the online schedule to see where my class was to be held (small classes often end up in surprise mystery buildings all over campus...I like this because I get to learn of new teaching spaces over in the Humanities territories, for example), and saw that the title of the course was something like "Introduction to Relativistic Field Theory". Hmmm.... problem there was that there is no course on the books entitled "String Theory, part II: Non-perturbative aspects", so the schedulers did the best they could. So I showed up for the first class (this is three weeks ago now), and sure enough, there are the six or seven graduate students from Nick's class.... but there are four or five students from the condensed matter group, and from the quantum information groups, part of CSI (I kid you not [update: you see, that's the group's name, see an earlier post]) over in Electrical Engineering! They saw a course with that title and, understandably, thought it was a good chance to learn some Relativistic Field Theory. So what to do.... Choices: (1) Treat the unprepared students (who have not done any field theory) as noise, and just carry on regardless? Plus point: I get to use my standard notes...little or no preparaton...more time for research.... Minus point: I can't bear to have people in my class who aren't getting anything out of it. It would drive me nuts! (2) Teach a Relativistic Quantum Field Theory course.... Plus point: Tony Zee's book is an excellent introduction; I've taught the second half before (to most of those folks from Nick' class) so it can't be too hard to make notes for the first half.... Minus point: the students and faculty high energy physics group (my people) would have me hung, drawn and quartered, and then taken out and shot with very slowly moving blunt bullets. (3) Do something else at the last minute. Well, I chose (3). Because I'm an idiot, I suppose. But it's a challenge. so I'm writing a whole new course as I go along...sometimes on the bus on the way to teach the class. What would the title be? I'm not sure yet, since I have no idea where I'm going, but I'm trying to put in a little bit for everybody from the three camps. They've agreed to be grown up and so some reading on each other's topics from time to time, to fill in a bit of background. So for example, the first day (since I abandoned my notes), we sat together and traded our recommendations for some of the best bits of background reading on topics in condensed matter theory, quantum information theory, and high energy theory. Next class, we traded mini explanations for what were central concepts in each topic that showed up in our reading.... all very touchy-feely. So in choosing (3), what am I lecturing on? Well, I'm trying to cut a path through some material that is of interest and value to several camps, no matter what area of theoretical physics you come from..... (apologies to the uninitiated for the unexplained terms in the next few paragraphs): So we started with the Ising model, and focussed on to phase transitions. Then we focused on the second order phase transition (a "critical point") and have lingered around that point for a while learning language of statistical physics, and converting it into bits of quantum field theory as well. We've understood the onset of scale invariance at such a point, (conformal invariance is to follow), and then scaling operators, critical exponents, the idea of irrelevant, relevant and marginal operators, their scaling dimensions, etc. Then we've taken a tour of various types of critical behaviour, understood the central idea of universal behaviour, critical exponents, scaling laws.....even discussed the fact that this shows up in real physics all over the place.... This week we learned about several of the fun things that theoretical physicists have done to define all sort of statistical models and phase transitions generalising the Ising model, such as the Potts models, the Lee-Yang model, etc....culminating in the RSOS/IRF models, built from the A-D-E Dynkin diagrams of the simply laced Lie algebras....this latter allowed me to digress on Lie Algebras, Dynkin diagrams and all that good stuff...sneakily introducing the diagrams for the affine cases too. Of course, little do they know what all this is leading up to....so much apparently specialized condensed matter physics and group theory is preparation for what I consider to be among the most interesting snd important topics in string theory too! Perturbative and non-perturbative. It'll sneak up on them in a rather nice way... This will lay the groundwork for more conformal field theory, and we'll worry about edge effects, and theories with boundary, and finite size effects....(so that'll be one way of understanding D-branes sneaking up in the background, among others.....) We'll also spend some time on various integrable systems (unpacking properties of things already seen above, and doing more), study solitons of various sorts, in various dimensions. Again, these will be all for their own sake, and will teach a lot about field theory....but there'll be important aspects of string theory just on the cusp of all of this too, and I'll bring this out when we're ready..... You know, it sounds like its a jumble of stuff, but there are some important themes, techniques and language that get sewn together by all this stuff, and gets left out of a lot of standard courses....I'm having fun just talking about the fun stuff I think that we're going to do.... So, it's time consuming, and it's a challenge to keep everyone catered for, but so far I think I've been up to the challenge.... three weeks gone, only another twelve or so of "winging it" to go! (None of them read this blog, so I think I'm safe....) -cvj