Nikolay Bogolyubov
Encyclopedia
Nikolay Nikolaevich Bogolyubov (another spelling Bogoliubov, , ; 21 August 1909, Nizhny Novgorod
– 13 February 1992, Moscow
) was a Russian
and Ukrainian
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).
, Russia
, in the family of a priest of Russian Orthodox Church
, teacher of theology
, psychology
and philosophy
Nikolay Mikhailovich Bogolyubov and Ol'ga Nikolaevna, teacher of music. The Soviet Union
regulations issued soon after the October Revolution
in 1917 did not allow for children of priests to obtain a good education, and in 1921 the family of Nikolay Bogolyubov moved to Kiev
, where these regulations did not work.
and soon started to work under the supervision of a famous mathematician Nikolay Krylov
. In 1924, at the age of 13, Nikolay Bogolyubov wrote his first published scientific paper On the behavior of solutions of linear differential equations at infinity. In 1925 he entered Ph.D. program at the Academy of Sciences of Ukrainian SSR
and obtained the degree of Kandidat Nauk (Candidat of Sciences, equivalent to Ph.D.) in 1928, at the age of 19, with the Ph.D. thesis On direct methods of variational calculus. In 1930, at the age of 21, he obtained the degree of Doktor nauk
(Doctor of Sciences, equivalent to Habilitation
), the highest degree in the Soviet Union, which requires to make a significant independent contribution to the science after Ph.D.
This early period of Bogolyubov's work in science was concerned with such mathematical problems as direct methods of the calculus of variations
, the theory of almost periodic function
s, methods of approximate solution of differential equation
s, and dynamical systems. This earlier research had already earned him wide recognition. One of his essays was awarded the Bologna Academy of Sciences Prize in 1930, and the author was awarded the erudite degree of doctor of mathematics '. This was the period when the great scientific rise of the young Nikolai Bogolyubov began, later producing new multiple scientific trends in modern mathematics, physics, and mechanics.
Since 1931, Krylov and Bogolyubov worked together on the problems of nonlinear mechanics and nonlinear oscillations. They were the key figures in the "Kiev school of nonlinear oscillation research", where their cooperation resulted in the paper "On the quasiperiodic solutions of the equations of nonlinear mechanics" (1934) and the book Introduction to Nonlinear Mechanics (1937; translated to English in 1947) leading to a creation of a large field of non-linear mechanics.
Distinctive features of the Kiev School approach included an emphasis on the computation of solutions (not just a proof of its existence), approximations of periodic solutions, use of the invariant manifolds in the phase space, and applications of a single unified approach to many different problems. From a control engineering
point of view, the key achievement of the Kiev School was the development by Krylov and Bogolyubov of the describing function
method for the analysis of nonlinear control problems.
In the period 1928—1973, Nikolay Bogolyubov worked in the Institute for Theoretical Physics of the National Academy of Sciences of Ukraine holding the position of the Director of the institute since 1965. He lectured in the Kiev University in the period 1936—1959.
against the Soviet Union
on 22 June 1941 (beginning of the Great Patriotic War
), most institutes and universities from west part of Russia were evacuated into east regions far from the battle lines. Nikolay Bogolyubov moved to Ufa
, where he became Head of the Departments of Mathematical Analysis at Ufa State Aviation Technical University
and at Ufa Pedagogical Institute, remaining on these positions during the period of July 1941 – August 1943.
(MSU). At that time the Head of the Department was Anatoly Vlasov
(for a short period in 1944 the Head of the Department was Vladimir Fock
). Theoretical physicists working in the department in that period included Dmitry Ivanenko, Arsenij Sokolov
, and other famous physicists.
In the period 1943–1946, Bogolyubov's resesarch was essentially concerned with the theory of stochastic process
es and asymptotic methods. In his work "?" a simple example of an anharmonic oscillator evolving under the force of the form as a superposition of incoherent sinusoidal oscillations with continuous spectrum was used to show that depending on a specific approximation time scale the evolution of the system can be either deterministic, or a stochastic process satisfying Fokker-Planck equation
, or even a process which is neither deterministic nor stochastic. In other words, he showed that depending on the choice of the time scale for the corresponding approximations the same stochastic process can be regarded as both dynamical and Markovian
, and in the general case as a non-Markov process. This work was the first to introduce the notion of time hierarchy in non-equilibrium statistical physics which then became the key concept in all further development of the statistical theory of irreversible processes.
In 1945, Bogolyubov proved a fundamental theorem on the existence and basic properties of a one-parameter integral manifold for a system of non-linear differential equations. He investigated periodic and quasi-periodic solutions lying on a one-dimensional manifold, thus forming the foundation for a new method of non-linear mechanics, the method of integral manifolds.
In 1946, he published in JETP two works on equilibrium and non-equilibrium statistical mechanics which became the essence of his fundamental monograph Problems of dynamical theory in statistical physics (Moscow, 1946).
On 26 January 1953, Nikolay Bogolyubov became the Head of the Department of Theoretical Physics at MSU, after Anatoly Vlasov decided to leave the position on January 2, 1953.
, axiomatic S-matrix theory, and works on the theory of dispersion relations.
In the late 1940s and 1950s, Bogoliubov worked on the theory of superfluid
ity and superconductivity
, where he developed the method of BBGKY hierarchy
for a derivation of kinetic equations, formulated microscopic theory of superfluidity, and made other essential contributions. Later he worked on quantum field theory
, where introduced the Bogoliubov transformation
, formulated and proved the Bogoliubov's edge-of-the-wedge theorem
and Bogoliubov-Parasyuk theorem
(with Ostap Parasyuk), and obtained other significant results. In the 1960s his attention turned to the quark
model of hadrons; in 1965 he was among the first scientists to study the new quantum number
color charge
.
In 1946, Nikolay Bogoliubow was elected as a Corresponding Member of the USSR Academy of Sciences
. In 1948, he became Academician
of the National Academy of Sciences of Ukraine and in 1953 Academician of the USSR Academy of Sciences.
(JINR), Dubna
, Russia, where he was a founder (together with Dmitry Blokhintsev) and the first director of the Laboratory of Theoretical Physics. This laboratory, where Nikolay Bogolyubov 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. Nikolay Bogolyubov was Director of the JINR in the period 1966—1988.
, Dmitry Shirkov
, Selim Krein, Iosif Gihman, Tofik Mamedov, Kirill Gurov
, Mikhail Polivanov, Naftul Polsky, Galina Biryuk, Sergei Tyablikov
, Dmitry Zubarev
, Vladimir Kadyshevsky, and many other students. His method of teaching, based on creation of a warm atmosphere, politeness and kindness, is famous in Russia and is known as the "Bogoliubov approach".
Joint Institute for Nuclear Research awards two prizes in memory of Nikolay Bogolyubov: The Bogolyubov Prize for scientists with outstanding contribution to theoretical physics and applied mathematics and the Bogolyubov Prize for young scientists. National Academy of Sciences of Ukraine awards the Bogolyubov Prize for scientists with outstanding contribution to theoretical physics and applied mathematics.
The central street of Dubna
is named in the memory of Nikolay Bogolyubov as Bogolyubov prospect .
Bogolyubov year
In 2009, the 100th anniversary of the birth of Nikolay Bogolyubov was celebrated with two conferences organized in the memory of Nikolay Bogolyubov in Russia and Ukraine:
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.
Statistical Mechanics:
Quantum Field Theory:
Selected works
Nizhny Novgorod
Nizhny Novgorod , colloquially shortened to Nizhny, is, with the population of 1,250,615, the fifth largest city in Russia, ranking after Moscow, St. Petersburg, Novosibirsk, and Yekaterinburg...
– 13 February 1992, Moscow
Moscow
Moscow is the capital, the most populous city, and the most populous federal subject of Russia. The city is a major political, economic, cultural, scientific, religious, financial, educational, and transportation centre of Russia and the continent...
) was a Russian
Russians
The Russian people are an East Slavic ethnic group native to Russia, speaking the Russian language and primarily living in Russia and neighboring countries....
and Ukrainian
Ukraine
Ukraine is a country in Eastern Europe. It has an area of 603,628 km², making it the second largest contiguous country on the European continent, after Russia...
Soviet mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and theoretical physicist
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
known for a significant contribution to quantum field theory
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
, classical and quantum statistical mechanics
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
, and to the theory of dynamical systems; a recipient of the Dirac Prize
Dirac Prize
The Dirac Prize is the name of four prominent awards in the field of theoretical physics, computational chemistry, and mathematics, awarded by different organizations, named in honour of Professor Paul Dirac, one of the great theoretical physicists of the 20th Century.- The Dirac Medal and Lecture...
(1992).
Early life (1909–1921)
Nikolay Bogolyubov was born on 21 August 1909 in Nizhny NovgorodNizhny Novgorod
Nizhny Novgorod , colloquially shortened to Nizhny, is, with the population of 1,250,615, the fifth largest city in Russia, ranking after Moscow, St. Petersburg, Novosibirsk, and Yekaterinburg...
, Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
, in the family of a priest of Russian Orthodox Church
Russian Orthodox Church
The Russian Orthodox Church or, alternatively, the Moscow Patriarchate The ROC is often said to be the largest of the Eastern Orthodox churches in the world; including all the autocephalous churches under its umbrella, its adherents number over 150 million worldwide—about half of the 300 million...
, teacher of theology
Theology
Theology is the systematic and rational study of religion and its influences and of the nature of religious truths, or the learned profession acquired by completing specialized training in religious studies, usually at a university or school of divinity or seminary.-Definition:Augustine of Hippo...
, psychology
Psychology
Psychology is the study of the mind and behavior. Its immediate goal is to understand individuals and groups by both establishing general principles and researching specific cases. For many, the ultimate goal of psychology is to benefit society...
and philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
Nikolay Mikhailovich Bogolyubov and Ol'ga Nikolaevna, teacher of music. The Soviet Union
Soviet Union
The Soviet Union , officially the Union of Soviet Socialist Republics , was a constitutionally socialist state that existed in Eurasia between 1922 and 1991....
regulations issued soon after the October Revolution
October Revolution
The October Revolution , also known as the Great October Socialist Revolution , Red October, the October Uprising or the Bolshevik Revolution, was a political revolution and a part of the Russian Revolution of 1917...
in 1917 did not allow for children of priests to obtain a good education, and in 1921 the family of Nikolay Bogolyubov moved to Kiev
Kiev
Kiev or Kyiv is the capital and the largest city of Ukraine, located in the north central part of the country on the Dnieper River. The population as of the 2001 census was 2,611,300. However, higher numbers have been cited in the press....
, where these regulations did not work.
Kiev (1921–?)
In Kiev Nikolay Bogolyubov began to actively study physics and mathematics. He attended research seminars in Kiev UniversityKiev University
Taras Shevchenko University or officially the Taras Shevchenko National University of Kyiv , colloquially known in Ukrainian as KNU is located in Kiev, the capital of Ukraine. It is the third oldest university in Ukraine after the University of Lviv and Kharkiv University. Currently, its structure...
and soon started to work under the supervision of a famous mathematician Nikolay Krylov
Nikolay Mitrofanovich Krylov
Nikolay Mitrofanovich Krylov was a Russian and Soviet mathematician known for works on interpolation, non-linear mechanics, and numerical methods for solving equations of mathematical physics.-Biography:...
. In 1924, at the age of 13, Nikolay Bogolyubov wrote his first published scientific paper On the behavior of solutions of linear differential equations at infinity. In 1925 he entered Ph.D. program at the Academy of Sciences of Ukrainian SSR
Ukrainian SSR
The Ukrainian Soviet Socialist Republic or in short, the Ukrainian SSR was a sovereign Soviet Socialist state and one of the fifteen constituent republics of the Soviet Union lasting from its inception in 1922 to the breakup in 1991...
and obtained the degree of Kandidat Nauk (Candidat of Sciences, equivalent to Ph.D.) in 1928, at the age of 19, with the Ph.D. thesis On direct methods of variational calculus. In 1930, at the age of 21, he obtained the degree of Doktor nauk
Doktor nauk
Doktor nauk is a higher doctoral degree, the second and the highest post-graduate academic degree in the Soviet Union, Russia and in many post-Soviet states. Sometimes referred to as Dr. Hab. The prerequisite is the first degree, Kandidat nauk which is informally regarded equivalent to Ph.D....
(Doctor of Sciences, equivalent to Habilitation
Habilitation
Habilitation is the highest academic qualification a scholar can achieve by his or her own pursuit in several European and Asian countries. Earned after obtaining a research doctorate, such as a PhD, habilitation requires the candidate to write a professorial thesis based on independent...
), the highest degree in the Soviet Union, which requires to make a significant independent contribution to the science after Ph.D.
This early period of Bogolyubov's work in science was concerned with such mathematical problems as direct methods of the calculus of variations
Calculus of variations
Calculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite integrals involving unknown...
, the theory of almost periodic function
Almost periodic function
In mathematics, an almost periodic function is, loosely speaking, a function of a real number that is periodic to within any desired level of accuracy, given suitably long, well-distributed "almost-periods". The concept was first studied by Harald Bohr and later generalized by Vyacheslav Stepanov,...
s, methods of approximate solution of differential equation
Differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...
s, and dynamical systems. This earlier research had already earned him wide recognition. One of his essays was awarded the Bologna Academy of Sciences Prize in 1930, and the author was awarded the erudite degree of doctor of mathematics '. This was the period when the great scientific rise of the young Nikolai Bogolyubov began, later producing new multiple scientific trends in modern mathematics, physics, and mechanics.
Since 1931, Krylov and Bogolyubov worked together on the problems of nonlinear mechanics and nonlinear oscillations. They were the key figures in the "Kiev school of nonlinear oscillation research", where their cooperation resulted in the paper "On the quasiperiodic solutions of the equations of nonlinear mechanics" (1934) and the book Introduction to Nonlinear Mechanics (1937; translated to English in 1947) leading to a creation of a large field of non-linear mechanics.
Distinctive features of the Kiev School approach included an emphasis on the computation of solutions (not just a proof of its existence), approximations of periodic solutions, use of the invariant manifolds in the phase space, and applications of a single unified approach to many different problems. From a control engineering
Control engineering
Control engineering or Control systems engineering is the engineering discipline that applies control theory to design systems with predictable behaviors...
point of view, the key achievement of the Kiev School was the development by Krylov and Bogolyubov of the describing function
Describing function
The Describing function method of Nikolay Mitrofanovich Krylov and Nikolay Bogolyubov is an approximate procedure for analyzing certain nonlinear control problems. It is based on quasi-linearization, which is the approximation of the non-linear system under investigation by an LTI system transfer...
method for the analysis of nonlinear control problems.
In the period 1928—1973, Nikolay Bogolyubov worked in the Institute for Theoretical Physics of the National Academy of Sciences of Ukraine holding the position of the Director of the institute since 1965. He lectured in the Kiev University in the period 1936—1959.
In evacuation (1941–1943)
After the German attackOperation Barbarossa
Operation Barbarossa was the code name for Germany's invasion of the Soviet Union during World War II that began on 22 June 1941. Over 4.5 million troops of the Axis powers invaded the USSR along a front., the largest invasion in the history of warfare...
against the Soviet Union
Soviet Union
The Soviet Union , officially the Union of Soviet Socialist Republics , was a constitutionally socialist state that existed in Eurasia between 1922 and 1991....
on 22 June 1941 (beginning of the Great Patriotic War
Great Patriotic War (term)
The term Great Patriotic War , Velíkaya Otéchestvennaya voyná,) is used in Russia and some other states of the former Soviet Union to describe the portion of World War II from 22 June 1941 to 9 May 1945, against Nazi Germany and its allies in the many fronts of Soviet-German war.-History:The term...
), most institutes and universities from west part of Russia were evacuated into east regions far from the battle lines. Nikolay Bogolyubov moved to Ufa
Ufa
-Demographics:Nationally, dominated by Russian , Bashkirs and Tatars . In addition, numerous are Ukrainians , Chuvash , Mari , Belarusians , Mordovians , Armenian , Germans , Jews , Azeris .-Government and administration:Local...
, where he became Head of the Departments of Mathematical Analysis at Ufa State Aviation Technical University
Ufa State Aviation Technical University
Ufa State Aviation Technical University is a state higher school, located in Ufa, Bashkortostan, Russia. Ufa State Aviation Technical University was founded in 1932 in Rybinsk, USSR. Nowadays, Ufa State Aviation Technical University has become the one of leading higher educational institutions of...
and at Ufa Pedagogical Institute, remaining on these positions during the period of July 1941 – August 1943.
Moscow (1943–?)
In autumn 1943, Bogolyubov came from evacuation to Moscow and on 1 November 1943 he accepted a position in the Department of Theoretical Physics at the Moscow State UniversityMoscow State University
Lomonosov Moscow State University , previously known as Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be one of the oldest university in Russia and to have the tallest educational building in the world. Its current rector is Viktor Sadovnichiy...
(MSU). At that time the Head of the Department was Anatoly Vlasov
Anatoly Vlasov
Anatoly Alexandrovich Vlasov was a Russian theoretical physicist prominent in the fields of statistical mechanics, kinetics, and especially in plasma physics.-Biography:...
(for a short period in 1944 the Head of the Department was Vladimir Fock
Vladimir Fock
Vladimir Aleksandrovich Fock was a Soviet physicist, who did foundational work on quantum mechanics and quantum electrodynamics....
). Theoretical physicists working in the department in that period included Dmitry Ivanenko, Arsenij Sokolov
Arsenij Sokolov
Arseny Alexandrovich Sokolov was a Russian theoretical physicist known for the development of synchrotron radiation theory.-Biography:Arseny Sokolov graduated from Tomsk State University in 1931. He obtained the degree of Kandidat nauk from TSU under supervision of Piotr Tartakovsky...
, and other famous physicists.
In the period 1943–1946, Bogolyubov's resesarch was essentially concerned with the theory of stochastic process
Stochastic process
In probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process...
es and asymptotic methods. In his work "?" a simple example of an anharmonic oscillator evolving under the force of the form as a superposition of incoherent sinusoidal oscillations with continuous spectrum was used to show that depending on a specific approximation time scale the evolution of the system can be either deterministic, or a stochastic process satisfying Fokker-Planck equation
Fokker-Planck equation
The Fokker–Planck equation describes the time evolution of the probability density function of the velocity of a particle, and can be generalized to other observables as well.It is named after Adriaan Fokkerand Max Planck...
, or even a process which is neither deterministic nor stochastic. In other words, he showed that depending on the choice of the time scale for the corresponding approximations the same stochastic process can be regarded as both dynamical and Markovian
Markov process
In probability theory and statistics, a Markov process, named after the Russian mathematician Andrey Markov, is a time-varying random phenomenon for which a specific property holds...
, and in the general case as a non-Markov process. This work was the first to introduce the notion of time hierarchy in non-equilibrium statistical physics which then became the key concept in all further development of the statistical theory of irreversible processes.
In 1945, Bogolyubov proved a fundamental theorem on the existence and basic properties of a one-parameter integral manifold for a system of non-linear differential equations. He investigated periodic and quasi-periodic solutions lying on a one-dimensional manifold, thus forming the foundation for a new method of non-linear mechanics, the method of integral manifolds.
In 1946, he published in JETP two works on equilibrium and non-equilibrium statistical mechanics which became the essence of his fundamental monograph Problems of dynamical theory in statistical physics (Moscow, 1946).
On 26 January 1953, Nikolay Bogolyubov became the Head of the Department of Theoretical Physics at MSU, after Anatoly Vlasov decided to leave the position on January 2, 1953.
Steklov Institute (1947–?)
In 1947, Nikolay Bogolyubov organized and became the Head of the Department of Theoretical Physics at the Steklov Mathematical Institute. In 1969, the Department of Theoretical Physics was separated into the Departments of Mathematical Physics (Head Vasily Vladimirov), of Statistical Mechanics, and of Quantum Field Theory (Head Mikhail Polivanov). While working in the Steklov Institute, Nikolay Bogolyubov and his school contributed to science with many important works including works on renormalization theory, renormalization groupRenormalization group
In theoretical physics, the renormalization group refers to a mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales...
, axiomatic S-matrix theory, and works on the theory of dispersion relations.
In the late 1940s and 1950s, Bogoliubov worked on the theory of superfluid
Superfluid
Superfluidity is a state of matter in which the matter behaves like a fluid without viscosity and with extremely high thermal conductivity. The substance, which appears to be a normal liquid, will flow without friction past any surface, which allows it to continue to circulate over obstructions and...
ity and superconductivity
Superconductivity
Superconductivity is a phenomenon of exactly zero electrical resistance occurring in certain materials below a characteristic temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum...
, where he developed the method of BBGKY hierarchy
BBGKY hierarchy
In statistical physics, the BBGKY hierarchy is a set of equations describing the dynamics of a system of a large number of interacting particles...
for a derivation of kinetic equations, formulated microscopic theory of superfluidity, and made other essential contributions. Later he worked on quantum field theory
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
, where introduced the Bogoliubov transformation
Bogoliubov transformation
In theoretical physics, the Bogoliubov transformation, named after Nikolay Bogolyubov, is a unitary transformation from a unitary representation of some canonical commutation relation algebra or canonical anticommutation relation algebra into another unitary representation, induced by an...
, formulated and proved the Bogoliubov's edge-of-the-wedge theorem
Edge-of-the-wedge theorem
In mathematics, Bogoliubov's edge-of-the-wedge theorem implies that holomorphic functions on two "wedges" with an "edge" in common are analytic continuations of each other provided they both give the same continuous function on the edge. It is used in quantum field theory to construct the...
and Bogoliubov-Parasyuk theorem
Bogoliubov-Parasyuk theorem
The Bogoliubov–Parasyuk theorem in quantum field theory states that renormalized Green's functions and matrix elements of the scattering matrix are free of ultraviolet divergencies. Green's functions and scattering matrix are the fundamental objects in quantum field theory which determine basic...
(with Ostap Parasyuk), and obtained other significant results. In the 1960s his attention turned to the quark
Quark
A quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
model of hadrons; in 1965 he was among the first scientists to study the new quantum number
Quantum number
Quantum numbers describe values of conserved quantities in the dynamics of the quantum system. Perhaps the most peculiar aspect of quantum mechanics is the quantization of observable quantities. This is distinguished from classical mechanics where the values can range continuously...
color charge
Color charge
In particle physics, color charge is a property of quarks and gluons that is related to the particles' strong interactions in the theory of quantum chromodynamics . Color charge has analogies with the notion of electric charge of particles, but because of the mathematical complications of QCD,...
.
In 1946, Nikolay Bogoliubow was elected as a Corresponding Member of the USSR Academy of Sciences
Russian Academy of Sciences
The Russian Academy of Sciences consists of the national academy of Russia and a network of scientific research institutes from across the Russian Federation as well as auxiliary scientific and social units like libraries, publishers and hospitals....
. In 1948, he became Academician
Academician
The title Academician denotes a Full Member of an art, literary, or scientific academy.In many countries, it is an honorary title. There also exists a lower-rank title, variously translated Corresponding Member or Associate Member, .-Eastern Europe and China:"Academician" may also be a functional...
of the National Academy of Sciences of Ukraine and in 1953 Academician of the USSR Academy of Sciences.
Dubna (1956–1992)
Since 1956, he worked in the Joint Institute for Nuclear ResearchJoint Institute for Nuclear Research
The Joint Institute for Nuclear Research, JINR , in Dubna, Moscow Oblast , Russia, is an international research centre for nuclear sciences, with 5500 staff members, 1200 researchers including 1000 Ph.D.s from eighteen member states The Joint Institute for Nuclear Research, JINR , in Dubna, Moscow...
(JINR), Dubna
Dubna
Dubna is a town in Moscow Oblast, Russia. It has a status of naukograd , being home to the Joint Institute for Nuclear Research, an international nuclear physics research centre and one of the largest scientific foundations in the country. It is also home to MKB Raduga, a defence aerospace company...
, Russia, where he was a founder (together with Dmitry Blokhintsev) and the first director of the Laboratory of Theoretical Physics. This laboratory, where Nikolay Bogolyubov worked for a long time, has traditionally been the home of the prominent Russian schools in quantum field theory
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
, theoretical nuclear physics
Nuclear physics
Nuclear physics is the field of physics that studies the building blocks and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those...
, statistical physics
Statistical physics
Statistical physics is the branch of physics that uses methods of probability theory and statistics, and particularly the mathematical tools for dealing with large populations and approximations, in solving physical problems. It can describe a wide variety of fields with an inherently stochastic...
, and nonlinear mechanics. Nikolay Bogolyubov was Director of the JINR in the period 1966—1988.
Family
His son Nikolay Boglyubov (jr) is a theoretical physicist working in the fields of mathematical physics and statistical mechanics.Students
Nikolay Bogoliubov was a scientific supervisor of Yurii MitropolskiyYurii Mitropolskiy
Yurii Alekseevich Mitropolskiy was a renowned Soviet, Ukrainian mathematician known for his contributions to the fields of dynamical systems and nonlinear oscillations. He received his Ph.D. from Kiev State University, under the supervision of theoretical physicist and mathematician Nikolay...
, Dmitry Shirkov
Dmitry Shirkov
Dmitry Vasil'evich Shirkov is a Russian theoretical physicist known for his contribution to quantum field theory and to the development of the renormalization group method.-Biography:...
, Selim Krein, Iosif Gihman, Tofik Mamedov, Kirill Gurov
Kirill Gurov
Kirill Gurov was a Soviet Russian theoretical physicist working in the field of physical kinetics.-Biography:Kirill Gurov was born in Moscow, Russia, in the family of a military officer...
, Mikhail Polivanov, Naftul Polsky, Galina Biryuk, Sergei Tyablikov
Sergei Tyablikov
Sergei Vladimirovich Tyablikov was a Russian theoretical physicist known for his significant contributions to statistical mechanics, solid-state physics, and for the development of the double-time Green function's formalism.-Biography:...
, Dmitry Zubarev
Dmitry Zubarev
Dmitry Nikolaevich Zubarev was a Russian theoretical physicist known for his contributions to statistical mechanics, non-equilibrium thermodynamics, plasma physics, theory of turbulence, and to the development of the double-time Green function's formalism....
, Vladimir Kadyshevsky, and many other students. His method of teaching, based on creation of a warm atmosphere, politeness and kindness, is famous in Russia and is known as the "Bogoliubov approach".
Awards
Nikolay Bogolyubov was a recipient of various high USSR honors and international awards, including- Stalin Prize (1947, 1953)
- USSR State PrizeUSSR State PrizeThe USSR State Prize was the Soviet Union's state honour. It was established on September 9, 1966. After the breakup of the Soviet Union, the prize was followed up by the State Prize of the Russian Federation....
(1984) - Lenin PrizeLenin PrizeThe Lenin Prize was one of the most prestigious awards of the USSR, presented to individuals for accomplishments relating to science, literature, arts, architecture, and technology. It was created on June 23, 1925 and was awarded until 1934. During the period from 1935 to 1956, the Lenin Prize was...
(1958) - Heineman Prize for Mathematical PhysicsDannie Heineman Prize for Mathematical PhysicsDannie Heineman Prize for Mathematical Physics is an award given each year since 1959 jointly by the American Physical Society and American Institute of Physics. It is established by the Heineman Foundation in honour of Dannie Heineman...
(1966) - Hero of Socialist LaborHero of Socialist LaborHero of Socialist Labour was an honorary title in the Soviet Union and other Warsaw Pact countries. It was the highest degree of distinction for exceptional achievements in national economy and culture...
(1969, 1979) - Max Planck medalMax Planck medalThe Max Planck medal is an award for extraordinary achievements in theoretical physics. It is awarded annually by the Deutsche Physikalische Gesellschaft , the world's largest organization of physicists.-List of recipients:...
(1973) - Franklin MedalFranklin MedalThe Franklin Medal was a science and engineering award presented by the Franklin Institute, of Philadelphia, PA, USA.-Laureates:*1915 - Thomas Alva Edison *1915 - Heike Kamerlingh Onnes *1916 - John J...
(1974) - The Lomonosov Gold Medal (1985)
- Dirac PrizeDirac PrizeThe Dirac Prize is the name of four prominent awards in the field of theoretical physics, computational chemistry, and mathematics, awarded by different organizations, named in honour of Professor Paul Dirac, one of the great theoretical physicists of the 20th Century.- The Dirac Medal and Lecture...
(1992)
Joint Institute for Nuclear Research awards two prizes in memory of Nikolay Bogolyubov: The Bogolyubov Prize for scientists with outstanding contribution to theoretical physics and applied mathematics and the Bogolyubov Prize for young scientists. National Academy of Sciences of Ukraine awards the Bogolyubov Prize for scientists with outstanding contribution to theoretical physics and applied mathematics.
The central street of Dubna
Dubna
Dubna is a town in Moscow Oblast, Russia. It has a status of naukograd , being home to the Joint Institute for Nuclear Research, an international nuclear physics research centre and one of the largest scientific foundations in the country. It is also home to MKB Raduga, a defence aerospace company...
is named in the memory of Nikolay Bogolyubov as Bogolyubov prospect .
Bogolyubov year
In 2009, the 100th anniversary of the birth of Nikolay Bogolyubov was celebrated with two conferences organized in the memory of Nikolay Bogolyubov in Russia and Ukraine:
- International Bogolyubov Conference: Problems of Theoretical and Mathematical Physics 21–27 August, Moscow-Dubna, Russia.
- Bogolyubov Kyiv Conference: Modern Problems of Theoretical and Mathematical Physics 15–18 September, KievKievKiev or Kyiv is the capital and the largest city of Ukraine, located in the north central part of the country on the Dnieper River. The population as of the 2001 census was 2,611,300. However, higher numbers have been cited in the press....
, Ukraine.
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
Bogoliubov causality condition
Bogoliubov causality condition is a causality condition for scattering matrix in axiomatic quantum field theory. The condition was introduced in axiomatic quantum field theory by Nikolay Bogolyubov in 1955.-Formulation:...
, obtained important results in quantum electrodynamics, and investigated on the basis of the edge-of-the-wedge theorem
Edge-of-the-wedge theorem
In mathematics, Bogoliubov's edge-of-the-wedge theorem implies that holomorphic functions on two "wedges" with an "edge" in common are analytic continuations of each other provided they both give the same continuous function on the edge. It is used in quantum field theory to construct the...
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 KrylovNikolay Mitrofanovich KrylovNikolay Mitrofanovich Krylov was a Russian and Soviet mathematician known for works on interpolation, non-linear mechanics, and numerical methods for solving equations of mathematical physics.-Biography:...
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.
- 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 KrylovNikolay Mitrofanovich KrylovNikolay Mitrofanovich Krylov was a Russian and Soviet mathematician known for works on interpolation, non-linear mechanics, and numerical methods for solving equations of mathematical physics.-Biography:...
gave the first consistent microscopic derivation of the Fokker-Planck equationFokker-Planck equationThe Fokker–Planck equation describes the time evolution of the probability density function of the velocity of a particle, and can be generalized to other observables as well.It is named after Adriaan Fokkerand Max Planck...
in the single scheme of classical and quantum mechanics. - 1945 Suggested the idea of hierarchy of relaxation timeRelaxation timeIn the physical sciences, relaxation usually means the return of a perturbed system into equilibrium.Each relaxation process can be characterized by a relaxation time τ...
s, 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 hierarchyBBGKY hierarchyIn statistical physics, the BBGKY hierarchy is a set of equations describing the dynamics of a system of a large number of interacting particles...
. - 1947 Jointly with K. P. GurovKirill GurovKirill Gurov was a Soviet Russian theoretical physicist working in the field of physical kinetics.-Biography:Kirill Gurov was born in Moscow, Russia, in the family of a military officer...
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 gasBose gasAn ideal Bose gas is a quantum-mechanical version of a classical ideal gas. It is composed of bosons, which have an integer value of spin, and obey Bose–Einstein statistics...
, 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 superconductivitySuperconductivitySuperconductivity is a phenomenon of exactly zero electrical resistance occurring in certain materials below a characteristic temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum...
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. ShirkovDmitry ShirkovDmitry Vasil'evich Shirkov is a Russian theoretical physicist known for his contribution to quantum field theory and to the development of the renormalization group method.-Biography:...
, 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 conditionBogoliubov causality conditionBogoliubov causality condition is a causality condition for scattering matrix in axiomatic quantum field theory. The condition was introduced in axiomatic quantum field theory by Nikolay Bogolyubov in 1955.-Formulation:...
for S—matrix in terms of variational derivatives. - 1955 Jointly with Dmitry ShirkovDmitry ShirkovDmitry Vasil'evich Shirkov is a Russian theoretical physicist known for his contribution to quantum field theory and to the development of the renormalization group method.-Biography:...
developed the renormalization groupRenormalization groupIn theoretical physics, the renormalization group refers to a mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales...
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 theoremBogoliubov-Parasyuk theoremThe Bogoliubov–Parasyuk theorem in quantum field theory states that renormalized Green's functions and matrix elements of the scattering matrix are free of ultraviolet divergencies. Green's functions and scattering matrix are the fundamental objects in quantum field theory which determine basic...
) 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 HanMoo-Young HanMoo-Young Han is a professor of physics at Duke University. Along with Yoichiro Nambu of the University of Chicago, he is credited with introducing the SU symmetry of quarks, today known as the color charge...
, Yoichiro NambuYoichiro Nambuis a Japanese-born American physicist, currently a professor at the University of Chicago. Known for his contributions to the field of theoretical physics, he was awarded a one-half share of the Nobel Prize in Physics in 2008 for the discovery of the mechanism of spontaneous broken symmetry in...
and Oscar W. GreenbergOscar W. GreenbergOscar Wallace Greenberg is an American physicist and professor at University of Maryland, College Park. He is famous for positing the existence of a property of subatomic particles called color charge.-Educational background:...
suggested a triplet quarkQuarkA quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
model and introduced a new quantum degree of freedom (later called as color chargeColor chargeIn particle physics, color charge is a property of quarks and gluons that is related to the particles' strong interactions in the theory of quantum chromodynamics . Color charge has analogies with the notion of electric charge of particles, but because of the mathematical complications of QCD,...
) for quarks. - Suggested a first proof of dispersion relations in quantum field theory.
Books
Mathematics and Non-linear Mechanics:- N. M. KrylovNikolay Mitrofanovich KrylovNikolay Mitrofanovich Krylov was a Russian and Soviet mathematician known for works on interpolation, non-linear mechanics, and numerical methods for solving equations of mathematical physics.-Biography:...
and N. N. Bogoliubov (1934): On various formal expansions of non-linear mechanics. Kiev, Izdat. Zagal'noukr. Akad. Nauk. - N. M. KrylovNikolay Mitrofanovich KrylovNikolay Mitrofanovich Krylov was a Russian and Soviet mathematician known for works on interpolation, non-linear mechanics, and numerical methods for solving equations of mathematical physics.-Biography:...
and N. N. Bogoliubov (1947): Introduction to Nonlinear Mechanics. Princeton, Princeton University Press. - N. N. Bogoliubov, Y. A. MitropolskyYurii MitropolskiyYurii Alekseevich Mitropolskiy was a renowned Soviet, Ukrainian mathematician known for his contributions to the fields of dynamical systems and nonlinear oscillations. He received his Ph.D. from Kiev State University, under the supervision of theoretical physicist and mathematician Nikolay...
(1961): Asymptotic Methods in the Theory of Non-Linear Oscillations. New York, Gordon and Breach.
Statistical Mechanics:
- N. N. Bogoliubov (1945): On Some Statistical Methods in Mathematical Physics. Kyiv .
- N. N. Bogoliubov, V. V. Tolmachev, D. V. ShirkovDmitry ShirkovDmitry Vasil'evich Shirkov is a Russian theoretical physicist known for his contribution to quantum field theory and to the development of the renormalization group method.-Biography:...
(1959): A New Method in the Theory of Superconductivity. New York, Consultants Bureau. - N. N. Bogoliubov (1960): Problems of Dynamic Theory in Statistical Physics. Oak Ridge, Tenn., Technical Information Service.
- N. N. Bogoliubov (1967—1970): 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 2-88124-879-9.
Quantum Field Theory:
- N. N. Bogoliubov, B. V. Medvedev, M. K. Polivanov (1958): Problems in the Theory of Dispersion Relations. Institute for Advanced Study, Princeton.
- N. N. Bogoliubov, D. V. ShirkovDmitry ShirkovDmitry Vasil'evich Shirkov is a Russian theoretical physicist known for his contribution to quantum field theory and to the development of the renormalization group method.-Biography:...
(1959): The Theory of Quantized Fields. New York, Interscience. The first text-book on the renormalization groupRenormalization groupIn theoretical physics, the renormalization group refers to a mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales...
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 978-0-8053-0982-9. ISBN 0-8053-0982-9.
- N. N. Bogoliubov, D. V. ShirkovDmitry ShirkovDmitry Vasil'evich Shirkov is a Russian theoretical physicist known for his contribution to quantum field theory and to the development of the renormalization group method.-Biography:...
(1980): Introduction to the Theory of Quantized Field. John Wiley & Sons Inc; 3rd edition. ISBN 0-471-04223-4. ISBN 978-0-471-04223-5. - N. N. Bogoliubov, D. V. ShirkovDmitry ShirkovDmitry Vasil'evich Shirkov is a Russian theoretical physicist known for his contribution to quantum field theory and to the development of the renormalization group method.-Biography:...
(1982): Quantum Fields. Benjamin-Cummings Pub. Co., ISBN 0-8053-0983-7. - 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. ISBN 0-7923-0540-X. ISBN 978-0-7923-0540-8.
Selected works
- N. N. Bogoliubov, Selected Works. Part I. Dynamical Theory. Gordon and Breach, New York, 1990. ISBN 2-88124-752-0, ISBN 978-2-88124-752-1.
- N. N. Bogoliubov, Selected Works. Part II. Quantum and Classical Statistical Mechanics. Gordon and Breach, New York, 1991. ISBN 2-88124-768-7.
- N. N. Bogoliubov, Selected Works. Part III. Nonlinear Mechanics and Pure Mathematics. Gordon and Breach, Amsterdam, 1995. ISBN 2-88124-918-3.
- N. N. Bogoliubov, Selected Works. Part IV. Quantum Field Theory. Gordon and Breach, Amsterdam, 1995. ISBN 2-88124-926-4, ISBN 978-2-88124-926-6.
Selected papers
- N. N. Bogoliubov (1948). "Equations of Hydrodynamics in Statistical Mechanics" (in Ukrainian). Sbornik Trudov Instituta Matematiki AN USSR 10: 41—59.
- "On Question about Superfluidity Condition in the Nuclear Matter Theory" (in Russian), 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.
See also
- Bogolyubov-Born-Green-Kirkwood-Yvon hierarchyBBGKY hierarchyIn statistical physics, the BBGKY hierarchy is a set of equations describing the dynamics of a system of a large number of interacting particles...
- Bogoliubov causality conditionBogoliubov causality conditionBogoliubov causality condition is a causality condition for scattering matrix in axiomatic quantum field theory. The condition was introduced in axiomatic quantum field theory by Nikolay Bogolyubov in 1955.-Formulation:...
- Bogolyubov's edge-of-the-wedge theorem
- Bogoliubov inner productBogoliubov inner productThe Bogoliubov inner product is a special inner product in the space of operators...
- Bogoliubov-Parasyuk theoremBogoliubov-Parasyuk theoremThe Bogoliubov–Parasyuk theorem in quantum field theory states that renormalized Green's functions and matrix elements of the scattering matrix are free of ultraviolet divergencies. Green's functions and scattering matrix are the fundamental objects in quantum field theory which determine basic...
- Bogoliubov transformationBogoliubov transformationIn theoretical physics, the Bogoliubov transformation, named after Nikolay Bogolyubov, is a unitary transformation from a unitary representation of some canonical commutation relation algebra or canonical anticommutation relation algebra into another unitary representation, induced by an...
- Describing function methodDescribing functionThe Describing function method of Nikolay Mitrofanovich Krylov and Nikolay Bogolyubov is an approximate procedure for analyzing certain nonlinear control problems. It is based on quasi-linearization, which is the approximation of the non-linear system under investigation by an LTI system transfer...
- Krylov-Bogoliubov averaging methodKrylov-Bogoliubov averaging methodThe Krylov–Bogolyubov averaging method is a mathematical method for approximate analysis of oscillating processes in non-linear mechanics. The method is based on the averaging principle when the exact differential equation of the motion is replaced by its averaged version...
- Krylov-Bogolyubov theoremKrylov-Bogolyubov theoremIn mathematics, the Krylov–Bogolyubov theorem may refer to any of the two related fundamental theorems within the theory of dynamical systems...
Further reading
- Yu. A. MitropolskiyYurii MitropolskiyYurii Alekseevich Mitropolskiy was a renowned Soviet, Ukrainian mathematician known for his contributions to the fields of dynamical systems and nonlinear oscillations. He received his Ph.D. from Kiev State University, under the supervision of theoretical physicist and mathematician Nikolay...
and S. V. TyablikovSergei TyablikovSergei Vladimirovich Tyablikov was a Russian theoretical physicist known for his significant contributions to statistical mechanics, solid-state physics, and for the development of the double-time Green function's formalism.-Biography:...
(1959). "Nikolai Nikolaevich Bogolyubov (on the occasion of his fiftieth birthday)". Soviet Physics Uspekhi, 2(5): 765—770. - D. N. ZubarevDmitry ZubarevDmitry Nikolaevich Zubarev was a Russian theoretical physicist known for his contributions to statistical mechanics, non-equilibrium thermodynamics, plasma physics, theory of turbulence, and to the development of the double-time Green function's formalism....
et al. (1970). "Nikolai Nikolaevich Bogolyubov (On his 60th birthday)", Soviet Physics Uspekhi, 12(4): 590—593. - V. S. Vladimirov et al. (1969). "Nikolai Nikolaevich Bogolyubov (on the occasion of his sixtieth birthday)", Russian Math. Surveys, 24(4): 167—175.
- V. A. Ambartsumyan et al. (1979). "Nikolai Nikolaevich Bogolyubov (on his seventieth birthday)", Soviet Physics Uspekhi, 22(8): 672—676.
- P. S. Aleksandrov et al. (1979). "Nikolai Nikolaevich Bogolyubov (on his seventieth birthday)", Russian Math. Surveys, 34(5): 1—10.
- A. A. Logunov, S. P. Novikov, V. S. Vladimirov (1989). "Nikolai Nikolaevich Bogolyubov (on his 80th birthday)", Russian Math. Surveys, 44(5): 1—10.
- A. A. AbrikosovAlexei Alexeyevich AbrikosovAlexei Alexeyevich Abrikosov is a Soviet and Russian theoretical physicist whose main contributions are in the field of condensed matter physics. He was awarded the Nobel Prize in Physics in 2003.- Biography :...
et al. (1989). "Nikolai Nikolaevich Bogolyubov (on his eightieth birthday)", Soviet Physics Uspekhi, 32(12): 1111—1112. - L. D. FaddeevLudvig Faddeev-References:...
et al. (1992). "Nikolai Nikolaevich Bogolyubov (obituary)". Russian Math. Surveys 47(3): 1—3 (in English). - D. V. Anosov (1994). "On the contribution of N.N. Bogolyubov to the theory of dynamical systems", Russian Math. Surveys, 49(5): 1—18.
- N. N. Bogolyubov (jr) and D. P. Sankovich (1994). "N. N. Bogolyubov and statistical mechanics". Russian Math. Surveys 49(5): 19—49.
- V. S. Vladimirov, V. V. Zharinov, A. G. Sergeev (1994). "Bogolyubov's “edge of the wedge” theorem, its development and applications", Russian Math. Surveys, 49(5): 51—65.
- O. I. Zav'yalov (1994). "Bogolyubov's R-operation and the Bogolyubov-Parasyuk theorem", Russian Math. Surveys, 49(5): 67—76.
- B. M. Levitan (1994). "On the work of Nikolai Nikolaevich Bogolyubov in the theory of almost periodic functions", Russian Math. Surveys, 49(5): 77—88.
- B. V. Medvedev (1994). "N.N. Bogolyubov and the scattering matrix", Russian Math. Surveys, 49(5): 89—108.
- A. M. Samoilenko (1994). "N.N. Bogolyubov and non-linear mechanics", Russian Math. Surveys, 49(5): 109—154.
- D. V. ShirkovDmitry ShirkovDmitry Vasil'evich Shirkov is a Russian theoretical physicist known for his contribution to quantum field theory and to the development of the renormalization group method.-Biography:...
(1994). "The Bogoliubov renormalization group". Russian Math. Surveys 49(5): 155—176. - V. S. Vladimirov (2001). "N. N. Bogoliubov and mathematics". Russian Math. Surveys 56(3): 607—613.
External links
- Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine.
- Bogolyubov Institute for Theoretical Problems of Microphysics at the Lomonosov Moscow State UniversityMoscow State UniversityLomonosov Moscow State University , previously known as Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be one of the oldest university in Russia and to have the tallest educational building in the world. Its current rector is Viktor Sadovnichiy...
, Russia. - Bogolyubov Laboratory of Theoretical Physics at the Joint Institute for Nuclear ResearchJoint Institute for Nuclear ResearchThe Joint Institute for Nuclear Research, JINR , in Dubna, Moscow Oblast , Russia, is an international research centre for nuclear sciences, with 5500 staff members, 1200 researchers including 1000 Ph.D.s from eighteen member states The Joint Institute for Nuclear Research, JINR , in Dubna, Moscow...
, Dubna, Russia. - Department of Theoretical Physics in the Steklov Mathematical Institute, Moscow, Russia (created by Nikolay Bogolyubov).
- The role of Nikolay Bogoliubov in Dubna's Russian Orthodox Christian church (in Russian).