Courtesy of AIP Niels Bohr Library

Paul A. M. Dirac

Y. S. Kim
Department of Physics, University of Maryland,
College Park, Maryland 20742, U.S.A.
(30 October 2002)

I met Paul A. M. Dirac in 1962 and 1978. In November of 1984, shortly after his death, I attended the memorial service held at Florida State University in Tallahassee, Florida. Eugene Wigner was his brother-in-law, and he told me many interesting stories about Dirac, especially about Mrs. Margit Dirac who was Wigner's younger sister.

Based on these contacts, I can write a story about Paul A. M. Dirac. Dirac is an important person to every physicist, perhaps in his/her own way. I would like to use this webpage to explain how my research life was affected by him. What is then so special about me? First of all, I maintain this webpage. Many people say that I do this webpage because I cannot do physics. Let us see.

In 1962, I was a first-year assistant professor at the University of Maryland, and John S. Toll was the chairman of the physics department. Toll invited Dirac to Maryland for three days, and I had to provide services to him. With him, I had one full hour to ask questions about physics. At that time, the only physics I knew, besides the basic knowledge to pass the PhD qualifying exam, was S-matrix theory or dispersion relations. In 1962, every particle theorist was doing the N/D (N over D) method (if you know this word, you are an old person these days). However, I was quite skeptical about the future of this program because it did not address fundamental issues.

Thus, I earnestly asked Dirac what the most pressing problem is in modern physics. He said that, in his opinion, physicists do not have a complete understanding of Lorentz covariance. He told me further that he had frustrating experiences when he attempted to clarify the difference between the invariance and covariance. I have to admit that Dirac could have been awfully frustrated if he had attempted to explain this difference to me at that time.

Even though I kept in mind what Dirac told me, I had to continue my research in S-matrix methods. Finally in 1965, I became totally disillusioned by those who were advocating this strange approach, after my frustrating experience with the Dashen-Frautschi fiasco . I decided not to trust them, and decided to pursue what Dirac told me in 1962.

I then studied Dirac's paper on "Forms of relativistic dynamics" published in the special issue of the Reviews of Modern Physics in commemoration of Einstein's 70th birthday published in 1949. I became fascinated by Dirac's light-cone system, and attempted to draw the pictures of ellipse in addition to hyperbolas usually associated with the Minkowskian world. The ellipse does not remain invariant. It changes its eccentricity, while the hyperbola remains invariant. In this way, I was able to understand the difference between the invariance and covariance.

Dirac was quite fond of harmonic oscillators. By 1973, in collaboration with Marilyn Noz of NYU, I was able to combine harmonic oscillators and Dirac's form of Lorentz transformations, and came up with this picture of Lorentz covariance. Indeed, since then, my entire research life has been centered around this circle-ellipse figure.

Since 1991, this figure appeared frequently on the posters on conferences on squeezed states, but its history goes back to what Dirac told me in 1962. Indeed, this figure is Dirac's gift to me.

In January of 1978, I met Dirac again while attending the Coral Gables conference held in Miami (Florida). At that time, I was quite confident about myself and asked him a number of specific questions. I had my own interpretation about "wiggly equality" signs in Dirac's 1949 paper, and wanted to confirm with what he originally had in mind.

Let us stop here talking about myself. If you are interested in how I am managing this circle-ellipse logo, you my click on it to see the details of my research program. If you wondered whether I am still doing physics, you will be interested to know I am still playing around with the circle-ellipse-hyperbola issue, as you can see from my latest paper (co-authored with Sibel Baskal).

In 1984, shortly after Dirac left us on October 20, 1984, I received an letter from Florida State University inviting me to the memorial convocation to be held on November 19. I went there and attended the service. I recall that Eugene Wigner spoke about how his younger sister became Mrs. Manci Dirac. Later, I heard directly from Wigner about his sisters. Indeed, I wrote about them for the proceedings of the 4th Wigner Symposium held in Guadalajara, Mexico held in 1995. Since then, I made a number of minor corrections, and added photos.

Please click here Wigner's sisters