Y. S. Kim's Research Program --- Overview

1. Einstein developed his relativistic dynamics for point particles. However, what happens when the particle has internal space-time degrees of freedom or an internal space-time extension? His energy-momentum relation, known as E = mc² , seems to work for all particles. Can then his special relativity explain the internal space-time symmetry and sapce-time extension? This has been and still is my main subject of interest. Click here for details.

   These days, some people say that we need a new Einstein (Einstein of the 21st-century) to solve the the mystery inside the relativistic extended particles. They even seem to have a number of candidates for this Einsteinship. I am grateful to them because they make my case clear to the world. My position is very simple. I like the original Einstein, and he prevails both in and outside the relativistic particle, and in the 21st century.

2. When Isaac Newton formulated his physical laws, he had to invent a new mathematics now called calculus. Not only in mechanics, calculus is the indispensable mathematical tool for all branches of science. When Einstein formulated relativity, he needed a new mathematics now called the Lorentz group. Thus, it is not crazy to expect that the Lorentz group is applicable to branches of physics other than relativity.

   It is remarkable that classical ray optics, as well as quantum optics, can be formulated in terms of the Lorentz group. Special relativity explains what happens in optics, and optics can provide analog computers for special relativity.

Here are more detailed stories.

I started my physics career with analytic properties of the S-matrix, but I was interested in explaining singularities in the complex plane in terms of wave functions. In so doing, I was able to explain the mistake Dashen made in his calculation of the neutron-proton mass difference in terms of wave functions. Click here if you are interested in what the controversy was about.

However, is the wave function a Lorentz-covariant concept? While struggling with this problem, R. P. Feynman in 1970, during the APS Washington meeting, gave an invited talk and came up with a suggestion that we should not use Feynman diagrams but use wave functions for relativistic bound states [Feynman, Kislinger, and Ravndal, Phys. Rev. D 3 , 2706 (1971)]. Feynman specifically suggested the use of harmonic oscillator wave functions. This is the origin of my research program.

First, I was interested in constructing normalizable harmonic oscillator wave functions. I constructed such wave functions in 1973. Using the covariant wave function, I solved in 1976 the question of whether the quark model and parton model are two different manifestations of one covariant entity. I regard this as my most significant contribution in physics. However, the physics community has been and still is very hostile to the result I published in 1977 [Phys. Rev. D 15 , 335 (1977)] and in 1989 [Phys. Rev. Lett. 63 , 348 (1989)].

How do I propose to solve this problem? Adiabatically! It would be most counter-productive if I shout around telling how the world is not treating me properly. The best I can do is to offer what is acceptable to my colleagues. For this purpose, I have been publishing papers which are more friendly to my colleagues, even though they are aimed at establishing a bridge between what I say in my 1977 paper with the rest of the world.

Since 1978, I have been writing articles about application of the Poincare group for relativistic extended hadrons. Inspired by Feynman, I have been using harmonic oscillator wave functions to construct the representation applicable to particles with space-time extensions. In 1986, together with Marilyn Noz, I published a book entitled "Theory and Applications of the Poincare Group." I then approached Eugene Wigner and carried out a collaboration with him until 1990 (Wigner was not able to think coherently after 1990). Together with him, I published seven papers and developed a conference series called "International Wigner Symposium."

I then found out my covariant harmonic oscillator formalism is directly applicable to quantum optics, especially to squeezed states of light. There is a conference series entitled "International Conference on Squeezed States and Uncertainty Relations," and I am still in charge of this IUPAP-sponsored program. The ultimate aim of this conference is to make my research result of 1977 known to the rest of the world. The circle/ellipse logo for this conference came from my 1973 paper with Noz [Phys. Rev. D 8 , 3521 (1973)].

My involvement in quantum optics led me to the field of foundations of quantum mechanics. There are many proposals in the literature about inventing new quantum mechanics. However, I strongly believe that we should understand the present form of quantum mechanics more thoroughly. For instance, the question of covariance is still at large. Do you know how to Lorentz-boost the hydrogen atom with its localized wave function? In order to understand this problem, we should face the question of the time-separation variable or time-like Bohr radius, which inevitably comes in whenever we try to Lorentz-boost the system.

Indeed, along with this new interest in foundations of quantum mechanics, the physics community introduced many new words. The word "decoherence" is a case in point. I am trying to present my earlier work on the quark-parton relation as a concrete example of the decoherence phenomenon.

In addition, it is fun to see that both classical and quantum optics can be formulated in terms of the Lorentz group. I am actively publishing in this field. I would like to write a book on this old-but-new subject. In recent years, I have established the Lorentz group is the basic underlying language for optical filters, interferometers, laser cavities, lens optics, and multilayer optics.

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