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[SQUEAKING] [RUSTLING] [CLICKING] [SIDE CONVERSATIONS] NORVIN RICHARDS: OK, so let's start back up. Today, let's see. We are transitioning from morphology into phonetics. So I hope you enjoyed morphology. It's not as if you won't ever do any morphology again. But that's it for lessons on morphology-- lectures, I guess. Today is phonetics, which means that today we begin making funny sounds at each other. So everybody limber up your vocal tracts. Let's see. I'm trying to remember if there's anything that I ought to announce. You remember, maybe, that problem set 1, which confusingly is your second problem set, is due on Thursday. Normally, it would be due on Tuesday. But because I am technologically challenged, it's due on Thursday. Speaking of being technologically challenged, I just figured out how to get the projector to project over there instead of in the middle so that I won't have to write everything twice running back and for...

[SQUEAKING] [RUSTLING] [CLICKING] [SIDE CONVERSATIONS] PROFESSOR: OK, let us start. So, last time, we discussed how to calculate such a correlation function, say Gn, in a single particle theory, so using path integral. So the goal is to calculate this time-ordered product correlation function, the vacuum correlation function, of this time-ordered product in this theory. So, last time, we described how to do this using path integral. And we derive the beautiful formula. So the formula is given by the following. It's a Gn is given by the ratio of two path integrals DX(t). So if we call this thing to be x. So the x and the exponential i S xt. And then, the DX(t), just the pure path integral. So, here, I didn't write to the upper limit and lower limit. So it should be understood that the boundary condition for both path integral is that the x-- So it should be from minus infinity-- the time range should be from minus infinity to plus infinity. And then we can choose t...