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

Einstein, Dirac, and Feynman

Both Dirac and Feynman were intensely interested in combining quantum mechanics with special relativity. Paul A. M. Dirac is known to us for his Dirac equation. Richard P. Feynman is known to us for Feynman diagrams. In fact, these two great physicists were interested in deeper foundational problems.

However, their approaches to physics were quite different. Dirac was interested in mathematical formulas with esthetic appeal. On the other hand, Feynman was interested in observing what is happening in the world and fill in mathematical formulas as needed.

Feynman's parton picture is one of his brilliant observations. Yet, this is valid in the infinite-momentum system and lacks Lorentz covariance. Thus, it is fun to look into the possibility of making it covariant by filling in mathematical formulas from Dirac's papers.

Photo by Bulent Atalay.

One way to do is to observe that both Dirac and Feynman were quite fond of harmonic oscillators because they satisfy Dirac's need for mathematical beauty, and also Feynman's need to fill in mathematical formulas readily available.

Dirac never liked the present form of quantum mechanics based on probabilistic interpretation. On the other hand, he held the view that,if we accept this interpretation, this form of quantum mechanics should be consistent with Lorentz covariance. Dirac published the following papers on this subject.

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

Photo by Harvey of Pasadena, Courtesy of the AIP Niels Bohr Library.

In his effort to combine quantum mechanics with relativity, Feynman first considered waves propagating in the Lorentz-covariant world, resulting in Feynman diagrams. How about standing waves? Feynman considered harmonic oscillators. Feynman would have liked to give a covariant description his parton picture, but left this problem as a homework problem for younger physicists. He wrote the following provocative papers on this subject.

1. 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).
2. R. P. Feynman, M. Kislinger, and F. Ravndal, Phys. Rev. D 3, 2706 (1971).
3. R. P. Feynman, Statistical Mechanics (Benjamin/Cummings, Reading, MA, 1972).

Recently, Kim and Noz produced a documentation on this issue and presented at an interdisciplinary science conference held in Natchitokes (Louisiana, October 2004). The paper is written for non-experts, and can be retrieved from the ArXiv.