Dirac and Feynman in One Box

Is it possible to translate this photo into physics? On this jubject, I published my first paper with Marilyn Noz in 1973.

I then wrote many other papers on the this subject with the following results.

>The issue is how to make quantum bound states consistent with special relativity. Do you know how the hydrogen atom with its electron orbit looks to a moving observer? Click here a story.

I was at the spot in 2013 where Dirac and Feynman met in 1962.

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.

• Yet, I am known in as Wigner's yougnest student in the physics world. How did this happen? Click here for a story. The point is that I started reading Wigner's 1939 paper when I was a graduate student at Princeton (1958-61), but started understading it only in 1978. In 1986, I published a book with Marilyn Noz on his paper. Wigner's 1939 paper deals with the internal space-time symmetries of particles in the Lorentz-covariant world. With this background, I approached Wigner 1985, and started to telling him the stories he wanted to hear.

• The following table shows how Dirac's papers and Feynman's papers can integrated into one big paper. Their papers can be translated into Wigner's language for the internal space-time symmetries of particles in the Lorentz-covariant world.

  Name of Physicist Dirac Feynman

  Means of Expression Mathematical Poems Cartoons and Diagrams

  Primary Interest Bound States, Standing Waves Scattering States, Running Waves

  Personality Seldom talks to anyone. Willing to join the crowd anywhere in the world.

  Favorite tools of research 4-by-4 matrices, Harmonic Oscillators Path integrals, Harmonic Oscillators

  What they did not see. Their physics can be formulated within the framework of Wigner's representation theory.

  Click here for soft spots in Dirac's papers and those in Feynman's papers. In Einstein's world, what problem are we dealing with?

• 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. Here are Dirac's papers which I studied in order to construct the Dirac-Feynman box.

  1. P. A. M. Dirac, The Quantum Theory of the Emission and Absorption of Radiation, Proc. Roy. Soc. (London) A [114], 243 - 265 (1927).

  2. P. A. M. Dirac, The Quantum Theory of the Emission and Absorption of Radiation, Proc. Roy. Soc. (London) A [A183], 284 - 295 (1945).

  3. P. A. M. Dirac, Forms of Relativistic Dynamics, Rev. Mod. Phys. [21] 392 - 399 (1949).

  4. P. A. M. Dirac, A Remarkable Representation of the 3 + 2 de Sitter Group, J. Math. Phys. [4], 901 - 909 (1963).

• At that time, he was working on the two-oscillator representation of the O(3,2) deSitter group, which later became the mathematical basis for two-mode squeezed states.
  Click here for an interesting story.

Richard P. 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.

  1. R. P. Feynman, Phys. Rev. Lett. 23, 1415 - 1417 (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 -2732 (1971).
  3. R. P. Feynman, Statistical Mechanics (Benjamin/Cummings, Reading, MA, 1972).

• Feynman Agenda. This webpage explains how thos Feynman papers could be coordinated.

Eugene P. Wigner

with Wigner (1986) with Treiman (1987)

I met Eugene Wigner while I was a graduate student at Princeton University. My thesis advisor was Sam Treiman. I wrote my thesis on dispersion relations which every bright had to study at that time. While working on my thesis, I had a question about the Lorentz covariance. I asked Wigner about the Lorentz frame with a fixed four-momentum. He said there are three degrees of freedom once the momentum is fixed. I did not realize he was talking about his 1939 paper on the little groups dictating the internal space-time symmetries.

• After 30 years, with Noz and Oh, I published my first paper on the representation of Wigner's little groups using harmonic oscillator wave functions. I needed a wave function that can be Lorentz-boosted in order to show that the quark model and the parton model are two different manifestation of one covariant entity, as indicated in the third row of the following table.

  Further contents of Einstein's E = mc2

  Massive/Slow between Massless/Fast

  Energy Momentum E=p2/2m Einstein's E=(m2 + p2)1/2 E=p

  Spin, Gauge, Helicity S3 S1 S2 Wigner's Little Group S3 Gauge Trans.

  Internal Space-time Gell-Mann's Quark Model Covariant Oscillators Feynman's Parton Picture

• In 1953, together with Inonu, Wigner published a paper on group contractions. Isaac Newton showed that a straight line tangential to a curve can play an important role in physics. How about a tangential plane on a curved surface. Inonu and Wigner addressed the question of a plane tangent on the north-pole of a sphere. They showed how the Galilean transformation emerges from the Lorentz transformation in the limit if slow speed. Here is a review paper by Inonu.

• Using this concept of group contractions, with Han and Kim in 1983, I published a paper in the Phys. Lett. B showing that the transverse rotational degrees become a gauge degree of freedom, as indicated in the second row of the above table.

  In 1986, with Marilyn Noz, I published a book entitled "Theory and Applications of the Poincaré Group." We completed tha manuscript in 1985. Here is a review of the book.

• Indeed, by 1985, I was prepared to tell Professor Wigner the stories he wanted to hear. I went to Princeton every two or three weeks to work with Wigner, and we together published seven papers. This is the reason why I am known as Wigner's youngest student.

• Symphony of Physics. Indeed, if we combine Dirac, Feynman, and Wigner, the net result is a physics symphony.