In fact, at a later stage, Professor Miyazawa pushed forward this idea by himself and became the inventor of supersymmetry.
In nineteen sixties the top topic was the group theory and the classification of elementary particles. Bunji Sakita, the inventor of the SU 6 theory, visited us at the University of Tokyo, and excited our interest in this theory. I noticed a beautiful parallelism between bose particles and fermi particles and wondered if they could be combined in one representation.
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Ignoring statistics, this is easy to do. All existing elementary particles can be expressed by the adjoint representation of the SU 9 group. Of course, I was not satisfied with this scheme since this only works for one particle states, i. I looked for a real mathematical scheme and soon found that a hamiltonian of the form. The set of all conserved quantities of these forms closes on commutators and anticommutators.
Thus I arrived at a new algebraic scheme with commutators and anticommutators. This paper was published in Progress of Theoretical Physics[ 2 ]. Since its publication I received some suggestions that by introducing anticommuting quantities the algebra can be reduced to an ordinary Lie algebra.
In such a scheme, one can construct only one particle state and no more. This is the case of Boltzmann statistics and I paid no attention to them. In I was at the University of Chicago, generalized the algebra to include the SU 6 and introduced an algebra which I called V 6, Here V meant beyond Unitary. I sent it to Physical Review[ 3 ]. The referee commented that this paper was very original and should be published in one form or another even though the result was not terribly interesting, and added that I should start from a simpler example.
Actually this was already done in my previous paper, so I stuck to the complicated model. While writing this paper I did not know how to call the algebra of this type.
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One day I called a professor of mathematics, Ichiro Satake, explained my algebra and asked him if such commutater—anticommutater algebra exists in the mathematical community. He replied that an algebra with anticommutators only was often called as Jordan algebra but he had never seen such a mixture. He was not interested in this algebra. About the same time I also explained this to Murray Gell-Mann who remarked: what is the all types of such algebra? The compact Lie groups are limited to a few cases, the orthogonal groups, unitary groups, symplectic groups and some exceptional ones.
Similarly, all types of the mixture algebra could be listed up.
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I regarded this an interesting mathematical problem. However, I wanted to try a more physical project, i. I tried first to write down an example of a relativistically invariant lagrangean that accepts boson-fermion symmetry. This was not easy, and before reaching the goal, I lost interest in this project. I thought that such relativistic boson-fermion symmetry now called supersymmetry could be formulated mathematically but it would not be the fundamental symmetry of physics.
If it were, the fundamental particles must consist of fermions and bosons. This contradicts the principle that the fundamental objects must be very few. In I became a postdoctoral fellow at Cornell University. A few months before I took the job, Adler 32 and Weissburger 33 independently published a very interesting work which showed that the framework of local field theory can be valid and even useful in understanding strong interactions. The basic idea is to use various local currents which can lead to the symmetry of interactions as a tool to study strong interaction.
This was so interesting that I started to use a slightly different technique regarding the current algebra and applied this to the process of non-leptonic hyperon decays; this was a process which I was familiar with since my graduate student work. I was able to reproduce some sum rules, 34 including the one which I had derived when I was a student. All the sum rules were experimentally verified and so I was convinced, together with many other theorists, that at least the basic framework of field theory must be correct.
What surprised me again here was that M. Suzuki, my classmate from the University of Tokyo, obtained the same result 35 using the same technique, although he was then at Caltech and I have no memory of us talking about this subject. We must have shared some philosophical attitude towards physics as students of Miyazawa. Gell-Mann 36 and G. Zweig 37 introduced the idea of the quark in as a purely mathematical object to explain the dynamics and symmetry of particle interactions. The successful use of current algebra in describing particle interactions led many researchers to the idea of using only currents, but not the quark field, as the fundamental objects of particle theory.
This idea looked quite adequate for quark theory since the quarks do not exist as a particle but as constituent of currents. At first, I was not clear what the framework should be. When C. Sommerfield of Yale University gave a talk at Berkeley and argued that the right way is to write the energy momentum tensor in terms of currents, I understood that it is the way to replace the conventional action theory.
Sommerfield did not show the form of the energy momentum tensor in terms of currents in a consistent way, so I started to work on this issue.
The first and foremost difficulty was to treat the so-called Schwinger term in current algebra. The simple Lagrangean model for quarks inevitably gave a diverging operator form for it. It was, therefore, useless if one wants to start from the explicit current algebra. After all kinds of trial and error, I finally succeeded in writing the energy-momentum tensor in terms of currents when we give up the q-number Schwinger term. But, I decided to publish the result. The reaction was more than I expected. I want to quote a statement from D. The hope was that the algebraic properties of the currents and the expression for the Hamiltonian in terms of these would be enough to have a complete theory.
Our goal was slightly more modest — to test the hypothesis by exploiting the fact that in this theory the operator product expansion of the currents contained the energy momentum tensor with a known coefficient. Thus we could derive a sum rule for the structure functions that could be measured in deep-inelastic electron-proton scattering . Eventually, however, the current-current Hamiltonian approach was replaced by more traditional Lagrangean formulation-QCD to which Y.
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Nambu, 14 G. Veltman, 15 D. Gross and F. Wilczek, 16 H. Politzer, 17 and many other people had contributed. The quark was supposed to be confined dynamically, rather than just being a mathematical object. The current-current Hamiltonian approach turned out to have a rather unexpected, but very interesting application in string theory. I quote the following statement by M. Around the same time, , after working for five years or so on current algebra, I suggested repeatedly that it would be wonderful if we could express the whole dynamics by means of current algebra, adjoining the energy density to the algebra of the internal charge and current densities, with the energy density expressed in terms of the charge and current densities, particularly in a light-cone frame.
In , in a bar in Ankara, I met Sugawara, who told me he had created such a model. I was delighted, but over time all of us became discouraged when we learned that it had really nice properties only in two dimensions. Today, as David Olive described so eloquently, such two-dimensional systems have turned out to be fundamental.
I should say that the current-current construction of the energy-momentum, which is usually called the Sugawara construction, should, in fact, be called Gell-Mann-Sommerfield-Sugawara construction, as all these people contributed to it in their own way. Most of the particle interactions became understandable within the framework of gauge theories. A surprisingly simple model of the weak and electromagnetic interactions by S. Weinberg 18 and A. Salam 19 turned out to be correct, as the discovery of neutral currents 39 dramatically demonstrated.
From the beginning my own interest was in studying the defects of the Standard Model: the Higgs interaction was not understood as gauge interaction and its origin is left untouched in the Standard Model. As a related problem, the question of the flavor degrees of freedom still remains. It was well known that CP symmetry cannot be violated in gauge interactions and that the Higgs interaction was the only way to violate CP symmetry within the Standard Model.
Kobayashi and T. Maskawa investigated this issue and proposed several versions to solve this problem. Pakvasa and I pursued their three quark version and studied its physical consequences. Maskawa: In their paper, they started by observing the fact that in this scheme with two families, there is no room for a non-trivial phase that could give rise to observable CP violation. The weak charged current for quarks is given by.
In Eq. But the three phases can be absorbed into the definition of three quark fields, and only the one mixing angle, the Cabibbo angle remains. They go on to try various options.
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One is to introduce a right handed doublet of quarks and leptons to preserve anomaly cancellation. In this case, there is indeed room for an extra phase which cannot be transformed away and can give rise to the observed CP violation in K decay. They observed that there are some phenomenological problems with such a scenario.
This possibility was raised and pursued already slightly earlier by Mohapatra, 14 who also found that there needs to be further proliferation of fields in such a model.
They also briefly considered other models with right handed currents and dismissed them as being not satisfactory. The second possibility is to increase the number of scalar fields beyond the minimal single Higgs doublet by one, and have two scalar fields. In this case also there is an extra phase which can give rise to CP violation.
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A few months earlier, Lee 15 had considered such a model in connection with a theory of spontaneous T violation. Finally, in the last page of the paper, they raise the third possibility of having three families of quarks and leptons. They give an explicit parameterisation of the matrix. In summer , when Hirotaka Sugawara arrived in Hawaii for his annual two month visit, he suggested that we work on CP violation, and specifically study the proposal in the K-M paper. We found that it was indeed possible to obtain a correct value for the K L decay rate with a reasonable choice of the new Cabibbo-like angles and the phase in the K-M matrix.