History of the Department
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
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).