Dirac and Feynman in One Box

Is it possible to translate this photo into physics. Click on the following figure.

Marek Holzman was a distinguished Polish photographer. In July of 1962, he produced this historic photo during the relativity conference held in Warsaw. This conference was organized by Leopold Infeld.

Since then, this photo has been a great inspiration to many physicists. As you know, I am a harmony man. Is it possible to find a harmony between these two great physicists?

More specifically, can Dirac's physics and Feynman's physics be put into one box to generate a new understanding or the world? How?

Both Dirac and Feynman made their life-long efforts to combine quantum mechanics with special relativity. Both of them used harmonic oscillators when they developed new ideas.

• Dirac wanted to understand physics by constructing mathematics, while Feynman started from what he observed in the real world. However their papers had weak spots. Their major weakness is the lack of figures.

  You have read Dirac's book entitled "Principles of Quantum Mechanics" where he introduced bra and ket vectors. Dirac's articles are like poems. But they do not contain figures.

• Feynman used to give brilliant lectures. He invented Feynman diagrams. Feynman was an established artist. He used to draw pictures on napkins at night clubs when he saw exciting things. However, he did not draw enough figures in his later papers. I do not know what went wrong with him. Perhaps his age.

  Like Feynman, I picked up the habit of drawing figures from John A. Wheeler. Feynman was Wheeler's thesis student at Princeton. Wheeler was not my advisor, but I was crazy enough to be remembered by him. Here is my Wheeler page. My advisor was Sam Treiman, who is known as Steven Weinberg's advisor.

In 1962, I was a first-year assistant professor at the University of Maryland when Dirac came, and I had to provide convenience to him. While I was alone with him, I asked him what the most important problem is in American physics and what I should study. I asked this question because I did not believe in what most of my colleagues were excited about at that time: bootstraps, N/D methods, strip approximations, just about one new word every week.

I was like Nicodemus who made a secret visit to Jesus in order to find out about himself.

Dirac's answer was that there are many things people do not understand about Lorentz invariance and Lorentz covariance. He was not talking about Chew or Mandelstam (headline makers at that time). I have been wondering about who was the person he had in mind. Recently, after studying Dirac's papers and Feynman's papers, I came to the conclusion that Dirac was talking about Feynman, especially in view of the fact that he was talking to me two months after he talked with Feynman as shown in this photo.

In addition, Dirac was telling me to study his own papers. At that time, he was working on the oscillator representation of the O(3,2) deSitter group, which later became the basic language for two-mode squeezed states. Here are Dirac's papers which I studied in order to construct the Dirac-Feynman box.

P. A. M. Dirac, Proc. Roy. Soc. (London) A114, 243 (1927). P. A. M. Dirac, Proc. Roy. Soc. (London) A183 , 284 (1945). P. A. M. Dirac, Rev. Mod. Phys. 21 , 392 (1949). P. A. M. Dirac, J. Math. Phys. 4 , 901 (1963).

Richard Feynman

My grandson is imitating Feynman.

Feynman's parton picture is one of his brilliant observations. Yet, this is valid only in the infinite-momentum system and lacks Lorentz covariance. Thus, it is fun to see whether the quark model and the parton model are two different manifestations of one Lorentz-covariant entity.

In 1970, at the spring meeting of the American Physical Society, Feynman gave a talk on the quark model based on a Lorentz-covariant harmonic oscillator formalism. Feynman talked about wave functions instead of Feynman diagrams. It was a surprise talk to all of of us, but it was the most important event in my life. Earlier, in 1966, I was thoroughly punished by some powerful people for using wave functions in one of my Phys. Rev. papers. Click here for the story. Indeed, Feynman gave me enough strength to stand firmly against the wind.

I studied the following papers before putting them into the Dirac-Feynman box.

R. P. Feynman, Phys. Rev. Lett. 23, 1415 (1969); R. P. Feynman, The Behavior of Hadron Collisions at Extreme Energies , in High Energy Collisions, Proceedings of the Third Topical Conference on High Energy Collisions of Hadrons, Stony Brook, New York, edited by C. N. Yang et al., Pages 237-249 (Gordon and Breach, New York, 1969). R. P. Feynman, M. Kislinger, and F. Ravndal, Phys. Rev. D 3, 2706 (1971). R. P. Feynman, Statistical Mechanics (Benjamin/Cummings, Reading, MA, 1972). Feynman Agenda. This webpage explains what Feynman attempted to do with these papers.

1. 1975. We were at Greenwich Village in New York.
2. 2006. We had a lunch together at New York's Oyster Bay restaurant in the basement of the Grand Central station.

Interesting Links

• Princeton Campus. I added many more photos to this webpage. The concept of "Campus" is very important to us. Greeks did not produce this word because they did not have big universities. Do you know who invented this word?

• Wigner's Sisters. Dirac's wife was Wigner's younger sister.

• Chaucer, Dirac, and Feynman on permutations.

• Feynman Photos. It is always fun to look at Feynman photos.