The God has created a man in order that he creates that the God fails to do

Monday, 10 October 2011

My Scientific Biography: Student period

In 1967, I graduated from the Moscow mathematical school №2 with a silver medal and entered Physics Faculty of Moscow State University. Besides the standard education program, I began to engage in self-education and went to the circle of theoretical physics, held for students of the junior courses of prof. D.Ivanenko, his staff and post-graduate students. I originally wanted to engage in theoretical physics, but at the faculty there were three theoretical departments. Under the influence of the theoretical circle, his broad topics, I decided to enter to the Department of Theoretical Physics to D.Ivanenko. From time to time, I even attended his scientific seminar.

In the middle of the third year, in spring of 1970, I was assigned to the Department of Theoretical Physics. The best students of the course tried to enter it, as well as on other theoretical departments. Only 12 people could do, and it was necessary to pass the interview. In the course of the interview, I felt that they knowingly take me: I had lost only on ball for all exam sessions and, apparently, D.Ivanenko warned that I am to him.

After entering the Department, I as a future graduate officially joined the group of Ivanenko: went to his scientific seminars, continued self-education, and eyed what anyone in the group is engaged in.

On the fourth course, I began to collaborate with Andrey Bulinski. He graduated from Physics Faculty in 1968, but was not taken in the graduate school and worked at the Department of Higher Mathematics of the Moscow Physical-Technical Institute. He continued to collaborate with D.Ivanenko, and engaged in algebraic quantum theory: algebras of quantum observables, their representations, quantum dynamical systems, etc. All of this was outside the scope of conventional courses of Physics Faculty. Working with him, I got a good experience in this field, which I then is very handy. In one of his articles, published in Journal of Theoretical and Mathematical Physics in 1971, he even thanking me for useful discussion. Although I do not remember that I was really any good. Algebraic quantum theory is rather mathematically sophisticated subject. My level was certainly not enough to get on this topic some original results and prepare a diploma work. Besides, Andrei Bulinski less and less began to come into the band and seminars of Ivanenko, apparently, having lost hope to return to Physics Faculty. Therefore, D.Ivanenko offered me, at least for pragmatic reasons, to change a research subject and a scientific chief (not being Ph.D., A.Bulinski formally could not be a scientific supervisor of my diploma work).

At that time, in science and seminars of Ivanenko, there has been actively discussed conformal field theory on the basis of the 15-parameter conformal group, including the Lorentz and Poincare subgroups. Naturally, the question arose about constructing the spinor representations of this group, as I did. My scientific supervisor was D.Sc. Dmitri Kurdgelaidze, a long-term employee of D.Ivanenko, with whom he developed a nonlinear meson and spinor theory. However, my purely algebraic subject was far away from his interest, and he could not help me. Therefore, I actually worked independently. I obtained a 8-spinor representation of the conformal group, which also implement the CPT transformations, and wrote for them the conformal-invariant Dirac equation. To me, this work still like it. I reported it on the 3-th Soviet gravitational conference in October 1972, and before that submitted an article to  "Vestnik of Moscow State University, Physics and Astronomy". However, for some reason, this article appeared much later, - in March of 1975. In January 1973, I defended my diploma work "Finite-dimensional  representations of the conformal group", with Ivanenko and Kurdgelaidze as supervisors.

To complete this topic, in 1973, I also constructed the nonlinear representation of the conformal group by the method of the so-called "nonlinear realizations". This method shortly before was developed, allowed to build a representation of a group as an extension of a representation of its Cartan subgroup, and was then very popular. This work was presented at the  Symposium "Modern problems of gravitation" in Moscow and went out in its Proceedings. It became my first scientific publication.

After graduating from the Physics Faculty February 1973, I in April was enrolled in the postgraduate school at the Department of Theoretical Physics to D.Ivanenko. My study of the conformal group was completed and, in front of me, there was a wide range of research directions. Interested in very many, D.Ivanenko provided a full freedom of activity of his graduate students. My direct supervisor was he himself, no one was standing between us, and I could do what I will.

First of all, I was interested in out-of-scope of the standard field theory on the basis of new mathematical methods of theoretical physics: algebraic, geometric and topological, because it was clear that the standard field theory had exhausted its possibilities. And I started with the search for and development of such innovative methods. Although the risk was great: could nothing is going to happen, no publications or dissertation. As it turned out, with the publication of problems was not, and that's Ph.D. thesis was delayed.

G. Sardanashvily: Scientific Biography

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