# Nikolay Bogolyubov : biography

**Nikolay Nikolayevich Bogolyubov** ( 21 August 1909 – 13 February 1992), also transliterated as **Bogoliubov**, was a Soviet mathematician and theoretical physicist known for a significant contribution to quantum field theory, classical and quantum statistical mechanics, and to the theory of dynamical systems; a recipient of the Dirac Prize (1992).

## Research

Fundamental works of Nikolay Bogoliubov were devoted to asymptotic methods of nonlinear mechanics, quantum field theory, statistical field theory, variational calculus, approximation methods in mathematical analysis, equations of mathematical physics, theory of stability, theory of dynamical systems, and to many other areas.

He built a new theory of scattering matrices, formulated the concept of microscopical causality, obtained important results in quantum electrodynamics, and investigated on the basis of the edge-of-the-wedge theorem the dispersion relations in elementary particle physics. He suggested a new synthesis of the Bohr theory of quasiperiodic functions and developed methods for asymptotic integration of nonlinear differential equations which describe oscillating processes.

### Mathematics and non-linear mechanics

- In 1932—1943, in the early stage of his career, he worked in collaboration with Nikolay Krylov on mathematical problems of nonlinear mechanics and developed mathematical methods for asymptotic integration of non-linear differential equations. He also applied these methods to problems of statistical mechanics.
- In 1937, jointly with Nikolay Krylov he proved the Krylov-Bogoliubov theorems. Zbl. 16.86.
- In 1956, at the International Conference on Theoretical Physics in Seattle, USA (September, 1956), he presented the formulation and the first proof of the edge-of-the-wedge theorem. This theorem in the theory of functions of several complex variables has important implications to the dispersion relations in elementary particle physics.

### Statistical mechanics

- 1939 Jointly with Nikolay Krylov gave the first consistent microscopic derivation of the Fokker-Planck equation in the single scheme of classical and quantum mechanics.N. N. Bogoliubov and N. M. Krylov (1939).
*Fokker-Planck equations generated in perturbation theory by a method based on the spectral properties of a perturbed Hamiltonian*. Zapiski Kafedry Fiziki Akademii Nauk Ukrainian SSR**4**: 81–157 (in Ukrainian). - 1945 Suggested the idea of hierarchy of relaxation times, which is significant for statistical theory of irreversible processes.
- 1946 Developed a general method for a microscopic derivation of kinetic equations for classical systems. The method was based on the hierarhy of equations for multi-particle distribution functions known now as Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy.
- 1947 Jointly with K. P. Gurov extended this method to the derivation of kinetic equations for quantum systems on the basis of the quantum BBGKY hierarchy.
- 1947—1948 Introduced kinetic equations in the theory of superfluidity, computed the excitation spectrum for a weakly imperfect Bose gas, showed that this spectrum has the same properties as spectrum of Helium II, and used this analogy for a theoretical description of superfluidity of Helium II.
- 1958 Formulated a microscopic theory of superconductivity and established an analogy between superconductivity and superfluidity phenomena; this contribution was discussed in details in the book
*A New Method in the Theory of Superconductivity*(co-authors V. V. Tolmachev and D. V. Shirkov, Moscow, Academy of Sciences Press, 1958).

### Quantum theory

- 1955 Developed an axiomatic theory for scattering matrix (
*S*—matrix) in quantum field theory and introduced the causality condition for*S*—matrix in terms of variational derivatives. - 1955 Jointly with Dmitry Shirkov developed the renormalization group method.
- 1955 Jointly with Ostap Parasyuk proved the theorem on the finiteness and uniqueness (for renormalizable theories) of the scattering matrix in any order of perturbation theory (Bogoliubov-Parasyuk theorem) and developed a procedure (R-operation) for a practical subtraction of singularities in quantum field theory.
- 1965 Jointly with Boris Struminsky and Albert Tavchelidze and independently of Moo-Young Han, Yoichiro Nambu and Oscar W. Greenberg suggested a triplet quark model and introduced a new quantum degree of freedom (later called as color charge) for quarks.N. Bogolubov, B. Struminsky, A. Tavkhelidze. On composite models in the theory of elementary particles. JINR Preprint D-1968, Dubna 1965.
- Suggested a first proof of dispersion relations in quantum field theory.