During the lectures at the Control Systems Laboratory during the summer, I doodled and thought about elementary particle theory. And I invented what was later called the Chelean representation [sic], representing the exact propagators for electron and photon in quantum field theory in... as integrals over virtual... over various masses, with weights for the masses. As you know this played an extremely important part later in the renormalization group work, and I noticed already that summer that, for the electron, the weights were both positive and negative, even though it looked as if you could prove they would always be positive. But in a theory with gauge invariants they didn't have to be positive for a charged particle. For a neutral particle they did, so the photon had positive weights and the electron had masses running over positive values and negative values, with the weights being sometimes positive and sometimes negative. I did all that, but I had no idea that that was a new contribution to theoretical physics, so I never told anybody or published it or anything – well, I must have told a few people but I didn't tell a great... I didn't give a seminar on it or... or publish it.
[Q] Did you have anything in mind?
And this was a year before Chelean, so it would have been my representation.
[Q] But were you thinking about quantum electrodynamics per se? I mean...
Field theory in general, including quantum electrodynamics, and I worked out the weights in quantum electrodynamics and saw that they were positive and negative. That was very important because years and years and years later that's how asymptotic freedom came to be recognized because the weights were... when, in Yang-Mills theory, which hadn't yet been invented in 1951, or discovered, whichever you want to call it, in Yang-Mills theory the quanta also have charges and therefore the quanta can have weights that are both positive and negative. And therefore the theorems about the photon that come from the purely positive weights in this representation no longer hold. And that's how you can have the opposite behavior in Yang-Mills theory from what you have in quantum electrodynamics. Anyway, I noted a lot of this and Francis [Low] and I put it into our paper, two, three years later, on what some people called the renormalization group. But actually I discovered it in 1951 while doodling…
[Q] That was also?
…while doodling at seminars at the Control Systems Laboratory.
[Q] The work with Francis was also in Urbana, right, so you must have returned?
It was also in Urbana, two years later, so I spent two summers in Urbana. Very, very, very hot weather in the summer, and only a few rooms were air-conditioned. The Control Systems Laboratory was air-conditioned for the equipment, of course.
[Q] Not for the people.
Right, and so that summer I had air-conditioning, and in ’53 Francis and I were sometimes allowed into air-conditioned rooms so we could think better. But it was only for equipment that people had air-conditioning at that time. Anyway, that was an example of how I actually discovered certain things but didn't realize they were of any importance. So in the fall of ’51 I could have written up this representation and then could have done work based on it and so on and so forth, but it never occurred to me to do that. Instead I kept looking ahead at things that I hadn't done and couldn't do, hoping that I could make progress on some important work.
