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[SQUEAKING] [RUSTLING] [CLICKING] DAVID KAISER: Today, we're now sort of in the middle of our unit of our last main unit on a kind of quarks to the cosmos, trends in high energy physics, astrophysics, and gravitation and cosmology. And so today, we'll be picking up part of the kind of threads that we were looking at before the Thanksgiving break, and we'll be looking in particular how was it and over what kind of time scale was it that most physicists came to be convinced that many, many types of matter are actually formed of quarks, that there's a constituent elementary unit within many kinds of matter. How did people come to be convinced of that and over what kind of time scale? So that's what we'll look at for part of today. So the three parts-- we'll revisit some of the trends that we already began looking at briefly, again, in the class sessions before the Thanksgiving break, in particular this what seemed to be a really unexpected and at ...

[SQUEAKING] [RUSTLING] [CLICKING] HONG LIU: OK, great. So now let's talk about QED. And OK. So let's first talk about QED. And we have talked about the Maxwell action. So here is the Lagrangian density. We have F mu nu minus J mu A mu, OK? And J mu should be a conserved current because for the consistency of the Maxwell equation, OK? Remember-- J mu has to be conserved. So now, the question is what provides this J mu, OK? So now, let's imagine. Now, let's introduce some other fields. Now, imagine we have some Dirac fermions. We have some fermionic field. Same with the Lagrangian. OK. So this is the Lagrangian for the Dirac fermion. And then we discussed that for Dirac fermion-- and then there's a conserved current because there's a global symmetry. There's a U1 symmetry corresponding to psi-- goes to exponential i alpha psi with alpha to be a constant. OK? And then this leads to a Noether current-- J mu, which is conserved. OK? So now, if we wa...