Laying Down the Lines

Yesterday was very busy for me, and a tiring day overall. It started with me getting up at 5:45am again, which was not so great this time since I went to sleep at 1:00am. The plan was to get to campus at 8:00am and continue writing my 10:00am lecture. This almost worked (I got delayed by half an hour due to sending more emails and so forth about the film competition) and I was at my desk at 8:30am, so only half an hour late. I’d been building most of the elements I needed for the class the night before, and in my head on the way, and so I had plenty of time.

Plenty of time for preparing fun since the lecture was the highlight of the day! I know it sounds odd, but I had a blast in that lecture! It was, as the cool kids say, Awesome! Now don’t get me wrong… I am not patting myself on the back about my lecturing skills… it is the material that was the star here, and if you put it together the right way, it simply shines. It did so yesterday. I’m teaching the introduction to quantum field theory, among the most powerful computational tools ever devised to study Nature. (The famous example brought up is this: What else allows you to compute a number to twelve significant figures, and check it against experiment to about the same accuracy? As Feynman said in his little book “QED”, it is like specifying the distance from New York to Los Angeles to the accuracy of the thickness of a human hair… (The number represents a property of an electron, and the computation is done in Quantum Electrodynamics, a form of quantum field theory.))

We’re starting to do self-interactions now, which require the development of something called perturbation theory. So I was showing how various ways of developing perturbation theory have different interpretations, and how they all tie together. In the end, we finished the two hour lecture (in which I got the students to try some bits of the computation) having computed numbers like 35/8 about four different ways. This included learning how to do it all using the combinatorics of cute little drawings called Feynman diagrams, which will turn out to be one of the most powerful tools in our arsenal in this class. The whole business can be boiled down to how you take line segments (called propagators) and glue them together using certain rules. Each resulting diagram represents a number, and you can work out that number by figuring out how many ways there are of making that diagram…. You can see some of the scribblings in the sample sketch I made for you this morning. (Click for larger view.)

Yes, it is on the back of an envelope… Another of the powerful traditional tools in the theoretical physicist’s arsenal.

Next week: Wick, Wick, and then Wick some more….

-cvj