Chaucer, Dirac, and Feynman

I cannot claim any expertise in English literature, especially on the literature before Shakespeare. However, I was able to enjoy one of the cinema versions of the Canterbury Tales. There one of the stories goes like this.

A shop keeper lives with his wife and a daughter. They sleep in a room with three double beds. The couple in one bed, and the daughter alone on the second bed with one empty spot. Then there come two male visitors who want to sleep in the shop keeper's house. They are invited to sleep on the third bed. During the night, one of the guests goes to bath room, but does not go back to his original bed, but to the empty spot on the daughter's bed. Sometime after, the shop keeper's wife goes to bath room and goes to the empty spot on the visitors' bed. I forgot what happened next, but the story goes on, and everybody is in his/her original position by the morning as if nothing had happened. In this particular tale, Chaucer was introducing the concept of permutation.

Photo by Bulent Atalay.

After seeing this movie in 1979, I was eager to see Paul A. M. Dirac to ask him whether he was inspired by Chaucer's Canterbury Tales when he was writing Section 55 of his book entitled "Principles of Quantum Mechanics" (very important book in physics). Dirac treats there permutations as dynamical operations with eigenvalues.

I was fortunate enough to talk with Dirac in 1962 and 1978 (before seeing the above-mentioned movie). In 1962, Dirac led me to the light-cone coordinate system. In 1978, I had questions about how to combine quantum mechanics and special relativity. Unfortunately, Dirac left us in 1984, and I was not able to talk with Dirac about Chaucer. However, I was invited to the memorial service held at Florida State University, and I attended. I thoroughly missed him, because I also wanted to talk about the following aspect of Richard Feynman.

In 1970, at the April meeting of the American Physical Society held in Washington, DC, Richard Feynman gave a talk on making the quark model relativistic and Lorentz-covariant. There he talked about construction of hadronic spectrum using three-dimensional harmonic oscillators, coupled with spins and unitary spins. With his students, namely Kislinger and Ravndal, Feynman published this talk in Phys. Rev. D, Volume 3, page 2706 (1971). In his talk (1970) and paper (1971), Feynman was using a permutation technique developed in Sec. 55 of Dirac's book.

It is not clear whether Feynman read this particular section of Dirac's book, but his mathematics was somewhat incomplete. With Paul Hussar and Marilyn Noz, I wrote a short note telling how the mathematics can be completed and submitted to the Physical Review D, but the paper was rejected. We then wrote a lengthy paper explaining what Feynman did starting from Dira'c Section 55. This paper was published in the American Journal of Physics.

Dirac and Feynman, courtesy of Caltech Photo Archives. License fee paid.

Both Dirac and Feynman were exceptionally creative physicists. They could formulate physical ideas from the phenomena to which ordinary people do not pay attention. As for the issue of whether Feynman studied Dirac's book, I can tell the following story.

In 1958, I was taking the first-year quantum mechanics while I was a senior (fourth-year undergraduate) at the Carnegie Institute of Technology (now called Carnegie-Mellon University). One of the homework problems was to read Secs. 55 and 56 of Dirac's book and work out three-particle symmetric states. The above-mentioned AJP paper was based on my solution to this homework problem.

The instructor was Michel Baranger who received his PhD degree from Cornell. Baranger had two advisors there. One was Hans Bethe, and the other was Richard Feynman. It was possible for Feynman and Baranger to have talked about Sec. 55 of Dirac's book.

Michel Baranger was kind enough to invite me and my wife to his retirement party held at MIT in 1997. We shared the dinner table with Francis Low and Victor Weisskopf. I had a photo with Baranger.

I have another story about him. If you are interested, you may click here.

Y.S.Kim (10 February 2004)