Nikolay Bogolyubov

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Nikolai Nikolaevich Bogoliubov
Born	21 August 1909(1909-08-21) Nizhny Novgorod, Russia
Died	February 13, 1992 (aged 82) Moscow, Russia
Nationality	Russia  Ukraine  USSR  Russia
Fields	Theoretical Physics, Mathematics
Institutions	Joint Institute for Nuclear Research, Dubna
Alma mater	Academy of Science of Ukrainian SSR Moscow State University
Doctoral advisor	Nikolay Krylov
Doctoral students	Dmitry Zubarev Sergei Tyablikov Dmitry Shirkov
Known for	significant contribution to quantum field theory, statistical mechanics, superconductivity, superfluidity; Bogoliubov transformation Bogoliubov edge-of-the-wedge theorem Krylov-Bogolyubov theorem BBGKY hierarchy
Notable awards	USSR State Prize (1947, 1953, 1984) Lenin Prize (1958) Hero of Socialist Labor (1969, 1979) Max Planck Medal (1973) Lomonosov Gold Medal (1985) Dirac Medal (1992).

Nikolay Nikolaevich Bogoliubov (Russian: Николай Николаевич Боголюбов, Ukrainian: Микола Миколайович Боголюбов) (21 August 1909, Nizhny Novgorod — 13 February 1992, Moscow) was a Russian and Ukrainian mathematician and theoretical physicist known for a significant contribution to quantum field theory, statistical field theory, and dynamical systems; a recipient of the Dirac Prize (1992).

[edit] Biography

Nikolay Bogoliubov was born in Nizhny Novgorod, Russia in 1909. His family moved to Kiev in 1921, where after graduation from a high school he began an independent study of mathematics and physics and attended seminars at the Kiev University. In 1924 he wrote his first published scientific paper. In 1925 he entered Ph.D. program at the Academy of Science of Ukrainian SSR, from which he graduated in 1929.

Nikolay Bogoliubov was a student of a famous Soviet mathematician Nikolay Mitrofanovich Krylov. Krylov and Bogoliubov were the key figures in what is called the Kiev School of nonlinear oscillation research. Their cooperation resulted in the paper "On the quasiperiodic solutions of the equations of nonlinear mechanics" (1934) and the book Introduction to Nonlinear Mechanics^{[book 1]} (1937; translated into English in 1947). Distinctive features of the Kiev School approach included an emphasis on the computation of solutions (not just proof of existence), on the approximation of periodic solutions, on invariant manifolds in phase space, and on applying similar methods to many different applications. From a control engineering point of view, the key achievement of the Kiev School was the development by Krylov and Bogoliubov of the describing function method for the analysis of nonlinear control problems.

In the late 1940s and 1950s Bogoliubov worked on the theory of superfluidity and superconductivity. Later he worked on quantum field theory, where in particular introduced the Bogoliubov transformation. In the 1960s his attention turned to the quark model of hadrons; in 1965 he was one of the first to study the new quantum number color charge.

Together with Dmitry Blokhintsev, Nikolay Bogoliubov was a founder and the first director of the Bogoliubov Laboratory of Theoretical Physics in the Joint Institute for Nuclear Research, Dubna, Russia. This laboratory, where Nikolay Bogoliubov worked for a long time, has traditionally been the home of the prominent Russian schools in quantum field theory, theoretical nuclear physics, statistical physics, and nonlinear mechanics.

[edit] Students

Nikolay Bogoliubov was a scientific supervisor^[1] of Yurii Mitropolskiy, Dmitry Shirkov, Selim Krein, Iosif Gihman, Naftul Polsky, Galina Biryuk, Sergei Tyablikov, Dmitry Zubarev, and many other students. His method of teaching, based on creation of a warmth atmosphere, politeness and kindness, is famous in Russia and is known as the "Bogoliubov approach".

[edit] 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.

[edit] 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 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.

[edit] Statistical mechanics

• 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.^{[paper 1][paper 2]} 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.^{[paper 3]}
• 1947—1948 Introduced kinetic equations in the theory of superfluidity.^{[paper 4]} He computed the excitation spectrum for a weakly imperfect Bose gas and showed that this spectrum has the same properties as spectrum of Helium II. This analogy was used for a theoretical description of supefluidity of Helium II.
• 1958 Formulated a microscopic theory of superconductivity^{[paper 5][book 2]} and established an analogy between superconductivity and superfluidity phenomena.

[edit] 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 substraction of singularities in quantum field theory.^{[paper 6][paper 7]}
• 1965 Independently suggested a triplet quark model and introduced the relevant notion of color charge for quarks.
• Suggested a first proof of dispersion relations in quantum field theory.

[edit] Fundamental publications

[edit] Books

References:

Mathematics and non-Linear Mechanics:

• N. N. Bogoliubov, Y. A. Mitropolsky (1961): Asymptotic Methods in the Theory of Non-Linear Oscillations. Gordon and Breach, New York.

Statistical Mechanics:

• N. N. Bogoliubov (1945): On Some Statistical Methods in Mathematical Physics. Kyiv (Russian).
• N. N. Bogoliubov (1960): Problems of Dynamic Theory in Statistical Physics. Oak Ridge, Tenn., Technical Information Service.
• N. N. Bogoliubov (1967-70): Lectures on Quantum Statistics. Problems of Statistical Mechanics of Quantum Systems. New York, Gordon and Breach.
• N. N. Bogolubov and N. N. Bogolubov, Jnr. (1992): Introduction to Quantum Statistical Mechanics. Gordon and Breach. ISBN 2881248799.

Quantum Field Theory:

• N. N. Bogoliubov, B. V. Medvedev, M. K. Polivanov (1958): Problems in the Theory of Dispersion Relations. Institute for Advanced Studies, Princeton.
• N. N. Bogoliubov, D. V. Shirkov (1959): The Theory of Quantized Fields. New York, Interscience. The first text-book on the renormalization group theory.
• N. N. Bogoliubov, A. A. Logunov and I. T. Todorov (1975): Introduction to Axiomatic Quantum Field Theory. Reading, Mass.: W. A. Benjamin, Advanced Book Program. ISBN 9780805309829. ISBN 0805309829.
• N. N. Bogoliubov, D. V. Shirkov (1980): Introduction to the Theory of Quantized Field. John Wiley & Sons Inc; 3rd edition. ISBN 0471042234. ISBN 9780471042235.
• N. N. Bogoliubov, D. V. Shirkov (1982): Quantum Fields. Benjamin-Cummings Pub. Co., ISBN 0805309837.
• N. N. Bogoliubov, A. A. Logunov, A. I. Oksak, I. T. Todorov (1990): General Principles of Quantum Field Theory. Dordrecht [Holland]; Boston, Kluwer Academic Publishers.

[edit] Selected papers

• "Equations of Hydrodynamics in Statistical Mechanics (in Russian), Sbornik trudov Instituta Matematiki AN CCCP, 10, 41, 1948.
• "On Question about Superfluidity Condition in the Nuclear Matter Theory", Doklady Akademii Nauk USSR, 119, 52, 1958.
• "On One Variational Principle in Many Body Problem" (in Russian), Doklady Akademii Nauk USSR, 119, N2, 244, 1959.
• "On Compensation Principle in the Method of Selfconformed Field" (in Russian), Uspekhi Fizicheskhih Nauk, 67, N4, 549, 1959.
• "The Quasi-averages in Problems of Statistical Mechanics" (in Russian), Preprint D-781, JINR, Dubna, 1961.
• "On the Hydrodynamics of a Superfluiding" (in Russian), Preprint P-1395, JINR, Dubna, 1963.

[edit] Awards

Nikolay Bogoliubov was a recipient of various USSR highest honors and international awards, including

• Hero of Socialist Labor (1969, 1979)
• Lenin Prize (1958)
• USSR State Prize (1947, 1953, 1984)
• The Lomonosov Gold Medal (1985)
• Max Planck medal (1973)
• Dirac Prize (1992)

Joint Institute for Nuclear Research awards two prizes in memory of Nikolay Bogoliubov: Bogoliubov Prize for scientists with outstanding contribution to theoretical physics and applied mathematics and the Bogoliubov Prize for young scientists.

[edit] See also

• Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy
• Bogoliubov causality condition
• Bogoliubov's edge-of-the-wedge theorem
• Bogoliubov inequality
• Bogoliubov — Parasyuk theorem
• Bogoliubov transformation
• Krylov-Bogoliubov theorem
• Hartree-Fock-Bogoliubov kinetic equations
• R-operation

[edit] References

[edit] External links

• Nikolay Bogolyubov at the Mathematics Genealogy Project
• Halanay, Aristide. "Book Review". Bulletin of the AMS. http://www.ams.org/bull/pre-1996-data/199430-1/halanay.pdf. 
• Shirkov D. V. The Bogoliubov Renormalization Group (English).
• N.N. Bogoliubov biography at the Joint Institute for Nuclear Research (Russian).
• N.N. Bogoliubov (Russian)
• Short information about N.N. Bogoliubov (Russian)
• The role of Nikolay Bogoliubov in Dubna's Russian Orthodox Christian church (Russian)

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