Department of Theoretical Physics

The Department of Theoretical Physics was organized at the Steklov Mathematical Institute in 1947, with N. N. Bogolyubov as the Head of Department. N. N. Bogolyubov invited to the Department many of his students and colleagues and in 1992, after more then forty years, there were already three Departments based on the Department of Theoretical Physics, namely, the Departments of Mathematical Physics, of Statistical Mechanics, and of Quantum Field Theory. The Department of Quantum Field Theory was organized in 1969, and until 1992 the Head of the Department was M. K. Polivanov. Since 1992, the Head of the Department is A. A. Slavnov. In 2002, the Department of Quantum Field Theory was reorganized as the Department of Theoretical Physics.

From the beginning, the main research area in the Department is the development of quantum field theory, especially its mathematical tools. The researchers working in the Department made a fundamental contribution to the development of quantum field theory and putting this theory into shape of the consistent theory with its own specific methods. The works of N. N. Bogolyubov and his school are of the utmost importance for this, namely, the works on renormalization theory, on renormalization group, on axiomatic S-matrix theory, and on the theory of dispersion relations. The corresponding results were summed up in the following monographs:

N. N. Bogolyubov and D. V. Shirkov,

Theory of Quantized Fields, Moscow, Gosud. Izdat. Tekhn.-Teor. Lit, 1957, 442 p.

N. N. Bogolyubov, B. V. Medvedev, and M. K. Polivanov,

Problems of the Theory of Dispersion Relations, Moscow, Fiz. Mat. Giz., 1958, 203 p. (Current Problems in Mathematics).

N. N. Bogolyubov, A. A. Logunov, I. T. Todorov, and A. I. Oksak,

Axiomatic Approach in Quantum Field Theory, Moscow, Nauka, 1969, 424 p.

O. I. Zavialov,

Renormalized Feynman Diagrams, Moscow, Nauka, 1979, 317 p.

Starting from the 1960s, the main progress in quantum field theory is associated with the development of gauge field theory. The gauge field theory gives an opportunity to describe all the known types of particle interactions from a unified geometrical point of view. Based on gauge field theory, the consistent theory of strong, weak and electro-weak interactions was constructed, which is known as Standard Model. At present, the most active researches are connected with constructing the unified theory that incorporate all types of interactions, including gravitation, and be based on models of relativistic strings which generalize gauge field theory to lengthy systems.

Pioneering investigations in quantum theory of gauge fields were carried out in the Department. Based on relations between Green functions, A. A. Slavnov constructed gauge invariant renormalization procedure known as `Slavnov–Taylor identities'. The first comprehensive exposition of the quantum gauge field theory was given in the monograph

A. A. Slavnov and L. D. Faddeev,

Introduction to Quantum Theory of Gauge Fields, Moscow, Nauka, 1978, 239 p.

Futher development of quantum field theory as whole is associated both with the perfection and profound study of methods of perturbation theory and with developing new methods which are not based on the perturbation expansions in terms of low coupling constant. Among these methods are lattice gauge theory, expansions in terms of number of colours in quantum chromodynamics, theory of completely integrable systems, and models of relativistic strings. The researchers working in the Department participate actively in these studies. Actual problems of quantum filed theory are discussed at the weekly working seminar of the Department. The members of the Department lecture at Moscow State University and Moscow Independent University, as well as are at the head of the students and the post graduate students works.

The main directions of scientific activity of the Department are as follows: quantum field theory, gauge fields, superstrings and branes, general theory of systems with constraints, non-perturbative methods, lattice models, completely integrable systems, conformally invariant theories, and matrix models.

The following topics are under active investigations:

• Problems of renormalization theory (A. A. Slavnov, I. Ya. Aref'eva, O. I. Zav'yalov).
• Theories of superstrings and D-branes, duality between gauge theories and superstring models (I. Ya. Aref'eva, G. Ed. Arutyunov, S. A. Frolov).
• Theory of systems with constraints (A. A. Slavnov, V. P. Pavlov).
• Completely integrable classical and quantum systems (A. K. Pogrebkov, N. A. Slavnov, L. O. Chekhov).
• Lattice models of quantum field theory (A. A. Slavnov, Yu. M. Zinoviev).