Nikolai Nikovaevich Bogolyubov – Great Scientist and Humanist of the XX-th Century
August 21, 2009 marked the hundredth anniversary of Nikolai Nikolaevich Bogoliubov,World Science Classic. Bogoliubov’s name entered forever the history of civilization. He was a Scientist of encyclopedic dimensions, one of the Creators of modern theoretical and mathematical physics, Founder of a con...
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irk-123456789-132972010-11-05T12:02:32Z Nikolai Nikovaevich Bogolyubov – Great Scientist and Humanist of the XX-th Century Golubjeva, O.N. Jenkovszky, L.L. Sukhanov, A.D. Хроніка, бібліографічна інформація, персоналії August 21, 2009 marked the hundredth anniversary of Nikolai Nikolaevich Bogoliubov,World Science Classic. Bogoliubov’s name entered forever the history of civilization. He was a Scientist of encyclopedic dimensions, one of the Creators of modern theoretical and mathematical physics, Founder of a constellation of scientific schools and of the widely known journal of Theoretical and Mathematical Physics. The logotype М∩Ф introduced by him, in Cyrillic, became the brand of a series of International Congresses on Mathematical Physics. (The last, XVI Congress of this series, was held in Prague, 2009, 3–8 August). The present paper is a short review of N.N. Bogoliubov’s life in science. His original papers, quoted in this review, can be found in [1]. For a colorful biography of the Master, we refer to Ref. [2]. 21 серпня 2009 року вiдзначалося столiття вiд дня народження Миколи Миколайовича Боголюбова – класика свiтової науки. Iм’я Боголюбова назавжди увiйшло в iсторiю цивiлiзацiї. Вiн був вченим енциклопедичного масштабу, одним з творцiв сучасної теоретичної i математичної фiзики, засновником сузiр’я наукових шкiл, а також широко вiдомого журналу “Теоретична i математична фiзика”. Логотип Ф∩М, запропонований ним, став знаком серiї мiжнародних конгресiв з математичної фiзики (останнiй, XVI-й Конгрес цiєї серiї вiдбувся у Празi 3–8 серпня 2009 року). Ця стаття є коротким оглядом основних наукових результатiв М.М. Боголюбова. Оригiнальнi роботи М.М. Боголюбова, якi згадуються в оглядi, можна знайти в його збiрцi творiв [1], а коротку бiографiю – в роботi [2]. 2010 Article Nikolai Nikovaevich Bogolyubov – Great Scientist and Humanist of the XX-th Century / O.N. Golubjeva, L.L. Jenkovszky, A.D. Sukhanov // Укр. фіз. журн. — 2010. — Т. 55, № 1. — С. 143-150. — Бібліогр.: 2 назв. — англ. 2071-0194 http://dspace.nbuv.gov.ua/handle/123456789/13297 en Відділення фізики і астрономії НАН України |
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Хроніка, бібліографічна інформація, персоналії Хроніка, бібліографічна інформація, персоналії |
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Хроніка, бібліографічна інформація, персоналії Хроніка, бібліографічна інформація, персоналії Golubjeva, O.N. Jenkovszky, L.L. Sukhanov, A.D. Nikolai Nikovaevich Bogolyubov – Great Scientist and Humanist of the XX-th Century |
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August 21, 2009 marked the hundredth anniversary of Nikolai Nikolaevich Bogoliubov,World Science Classic. Bogoliubov’s name entered forever the history of civilization. He was a Scientist of encyclopedic dimensions, one of the Creators of modern theoretical and mathematical physics, Founder of a constellation of scientific schools and of the widely known journal of Theoretical and Mathematical Physics. The logotype М∩Ф introduced by him, in Cyrillic, became the brand of a series of International Congresses on Mathematical Physics. (The last, XVI Congress of this series, was held in Prague, 2009, 3–8 August). The present paper is a short review of N.N. Bogoliubov’s life in science. His original papers, quoted in this review, can be found in [1]. For a colorful biography of the Master, we refer to Ref. [2]. |
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Golubjeva, O.N. Jenkovszky, L.L. Sukhanov, A.D. |
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Golubjeva, O.N. Jenkovszky, L.L. Sukhanov, A.D. |
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Golubjeva, O.N. |
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Nikolai Nikovaevich Bogolyubov – Great Scientist and Humanist of the XX-th Century |
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Nikolai Nikovaevich Bogolyubov – Great Scientist and Humanist of the XX-th Century |
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Nikolai Nikovaevich Bogolyubov – Great Scientist and Humanist of the XX-th Century |
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Nikolai Nikovaevich Bogolyubov – Great Scientist and Humanist of the XX-th Century |
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Nikolai Nikovaevich Bogolyubov – Great Scientist and Humanist of the XX-th Century |
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nikolai nikovaevich bogolyubov – great scientist and humanist of the xx-th century |
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Відділення фізики і астрономії НАН України |
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Хроніка, бібліографічна інформація, персоналії |
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Nikolai Nikovaevich Bogolyubov – Great Scientist and Humanist of the XX-th Century / O.N. Golubjeva, L.L. Jenkovszky, A.D. Sukhanov // Укр. фіз. журн. — 2010. — Т. 55, № 1. — С. 143-150. — Бібліогр.: 2 назв. — англ. |
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CHRONICLE, BIBLIOGRAPHIC DATA, AND PERSONALIA
ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 1 143
NIKOLAI NIKOLAEVICH BOGOLIUBOV – GREAT
SCIENTIST AND HUMANIST OF THE XX-TH CENTURY
O.N. GOLUBJEVA,1 L.L. JENKOVSZKY,2 A.D. SUKHANOV3
1Russian Peoples’ Friendship University
(Moscow, Russia)
2Bogolyubov Institute for Theoretical Physics of the NAS of Ukraine
(14b, Metrolohichna Str., Kyiv 03143, Ukraine)
3Bogoliubov Lab. Theor. Physics, JINR
(Dubna 141980, Moscow region, Russia)c©2010
August 21, 2009 marked the hundredth anniversary of Nikolai
Nikolaevich Bogoliubov, World Science Classic. Bogoliubov’s name
entered forever the history of civilization. He was a Scientist of
encyclopedic dimensions, one of the Creators of modern theoreti-
cal and mathematical physics, Founder of a constellation of scien-
tific schools and of the widely known journal of Theoretical and
Mathematical Physics. The logotype М∩Ф introduced by him, in
Cyrillic, became the brand of a series of International Congresses
on Mathematical Physics. (The last, XVI Congress of this series,
was held in Prague, 2009, 3–8 August).
The present paper is a short review of N.N. Bogoliubov’s life in
science. His original papers, quoted in this review, can be found
in [1]. For a colorful biography of the Master, we refer to Ref. [2].
Il libro della natura é scritto in lingua matematica.
Galileo Galilei
1. The Master
Bogoliubov was born in Nizhnii Novgorod to a highly ed-
ucated family, giving the world three academicians. His
father, Nikolai Mikhailovich Bogoliubov, was a promi-
nent priest, philosopher and theologian, possessing en-
cyclopedic knowledge – both in natural sciences and the
humanities. The father played a decisive role in the early
development of mathematical abilities of his son.
Already during his life, a myth (also connected with
N. Wiener) existed, according to which a team of mathe-
maticians, mechanics, and theoretical physicists worked,
alias “N.N. Bogoliubov”, similar to the known Bourbaki
group.
Really, it is difficult to conceive how could one man
create so many outstanding works in such different sci-
entific branches. The proper word marking a scientist
of such dimensions is genius. The organic cohesion of
mathematics, mechanics, and physics, inherent in Bo-
goliubov, places his name near the greatest thinkers of
the past – Newton, Euler, and Poincaré.
O.N. GOLUBJEVA, L.L. JENKOVSZKY, A.D. SUKHANOV
Bogoliubov’s range among XX-th century scientists
was established long ago. It was generally accepted that
his research stimulated the creation of the unique charac-
ter of the modern theoretical and mathematical physics,
unifying the power of the mathematical logic with the
profundity of the physical intuition.
2. Mathematical Genius
Bogoliubov’s carrier begun in Kiev under the guidance of
Academician N.M. Krylov. At the age of 15, Nikolai pro-
duced his first mathematical work. One of his important
early papers was dedicated to a new direct method of
variation calculus for nonregular functionals, and it con-
tained a number of original solutions to the ideas of the
Italian mathematician L. Tonelli. By Tonelli’s presenta-
tion, this paper was awarded the Bologna Academy of
Science’s prize in 1930, and the author was consecrated
into Doctor of Mathematics honoris causa.
This, initial period of Bogoliubov’s scientific carrier,
was dedicated to theoretical and applied mathematical
problems. For example, he suggested a new construc-
tion of the theory of almost periodic functions. During
this period, Bogoliubov and Krylov (1937) presented the
first proof of the famous theorem of the existence of the
invariant measure in dynamical systems.
After World War II, Bogoliubov’s remarkable papers
in modern mathematics appeared, by building the ap-
paratus to solve new problems in theoretical physics.
Note that proving theorems was never his mathematical
hobby, instead he did so always ad hoc. He contributed
to the solution of the most difficult mathematical prob-
lems of quantum field theory, thus changed the tradi-
tional view of the connection between mathematics and
physics.
Such is the “edge of the wedge” theorem (Seattle, 1956)
formulated and proved by him, as well as its generaliza-
tions and corollaries derived by his disciples and follow-
ers. It became a basic part of mathematics, opening a
new successful part of the theory of analytic functions.
The paper “On the self-similar asymptotics in quantum
field theory” (1972, with V.S. Vladimirov, A.N. Tavkhe-
lidze) initiated a new line of research in mathematics
– the multidimensional Tauberian theory of generalized
functions.
The R-operation suggested by Bogoliubov to remove
ultraviolet divergences from Feynman diagrams and the
theorem proved together with O.S. Parasiuk (1955) is
among the most important contributions of Bogoliubov
to quantum field theory. It has solved the crucial prob-
lem of the very existence of quantum field theory.
3. Nonlinear Mechanics as a New Branch in
Science and Technology
Since 1932, Bogoliubov, in collaboration with Krylov,
began developing an entirely new branch of mathemat-
ical physics, they called “nonlinear mechanics”. These
studies were carried out in two directions: developing
a new asymptotic integration techniques of nonlinear
equations of motion in oscillatory systems and laying a
foundation for these methods based on measure theory.
Krylov and Bogoliubov extended the tools of pertur-
bation theory to more general nonconservative systems,
and they created new and well established asymptotic
methods of nonlinear mechanics. Unlike the popular
van der Pol’s method, the corresponding solutions could
be obtained not only in the first but in higher approxi-
mations as well. These methods became very useful in
the studies of both periodic and quasiperiodic oscillatory
processes.
Applying the Lyapunov–Poincaré and the Poincaré–
Denjoy theory of trajectories on the torus, they stud-
ied the nature of an exact stationary solution near
the approximate solution for a small parameter value
and established the existence and stability theorems for
quasiperiodic solutions.
Furthermore, the development of efficient methods of
asymptotic integration for a wide class of nonlinear equa-
tions culminated, due to Bogoliubov and Krylov, in fun-
damental results. Bogoliubov also created new mathe-
matical tools to study the behavior of general noncon-
servative systems with small parameter. The fundamen-
tal averaging principle was formulated and developed
by Bogoliubov in the context of standard form equa-
tions (1945) and published in the monograph “Asymp-
totic Methods in the Theory of Nonlinear Oscillations”
(in collaboration with Yu.A. Mitropol’skii, 1955).
In 1945, Bogoliubov also proved the fundamental exis-
tence theorem on main properties of a single-parametric
integral manifold for a system of nonlinear differential
equations in the standard form. He investigated peri-
odic and quasiperiodic solutions on a one-dimensional
manifold – the essence of a new method in nonlinear
mechanics – the “method of integral manifolds”.
In 1963, Bogoliubov has put forward a new idea on the
application of the accelerated convergence techniques to
nonlinear mechanics. In establishing this theory, Bo-
goliubov combined the method of integral manifolds
with the iteration method by A.N. Kolmogorov and
V.I. Arnold. This combined method gave rise to yet
another method of accelerated convergence in nonlinear
mechanics.
144 ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 1
NIKOLAI NIKOLAEVICH BOGOLIUBOV
4. Towards the Unified Description of the
Nature
The above-mentioned achievements alone could be suf-
ficient to immortalize Bogoliubov’s name in the history
of science. Yet, these investigations were merely a start-
ing point for his further activity. As Bogoliubov wrote,
“these methods appeared to be so flexible that it be-
came possible to extend them later on beyond the scope
of nonlinear mechanics per se and to use in completely
other fields – in statistical physics, theory of kinetic
equations, quantum field theory, etc.”.
In the late 1930s, relying on the established math-
ematical foundation, Bogoliubov set to realize his ap-
proach to the description of the Nature. Later on, that
approach largely contributed to the birth of the modern
theoretical and mathematical physics. One of his first
universal ideas was the concept of maximal conceptual
proximity of the description of the Nature at classical
and quantum levels.
This idea was first implemented by him in collab-
oration with Krylov in the comprehensive paper “On
Fokker–Planck equations, application to classical and
quantum mechanics” (1939). This paper contained a re-
search program that basically predetermined the future
scientific work of Bogoliubov and his disciples in statis-
tical mechanics and quantum theory.
Its global aim is to open the way for the revision of the
basic principles of the theory of stochastic systems inter-
preted in the broad sense of the word. In authors’ opin-
ion, the main attention in this theory should be paid to
the description of weak, random effects on the considered
relatively small object induced by the environment as a
system with an infinite number of degrees of freedom.
According to Bogoliubov and Krylov, even though the
random effects are of both thermal and quantum types,
it is most important that the results of these effects, as
was earlier suggested by Einstein, can be described uni-
formly.
Bogoliubov’s next major work was the monograph
“On Some Statistical Methods in Mathematical Physics”
(1945) which was, in essence, a direct continuation of the
1939 paper. Of extreme importance in the evolution of
statistical physics was the result produced by Bogoliubov
in Chapter IV of the 1945 book, where he considered a
model example which allowed a detailed study of the
emergence of an irreversible macroscopic process when
an object approaches the state of thermal equilibrium.
By analyzing the problem of thermostat modeling, Bo-
goliubov was the first who noticed that the model tradi-
tionally used in quantum statistical mechanics is a clas-
sical one. As a result of this study, it was shown for the
first time strictly that, on a long-time scale, the prob-
ability distribution for the coordinate and momentum
of the considered object also came close to the Gibbs
equilibrium canonical distribution with the thermostat
temperature. In other words, the characteristics of the
object that were dynamical at the beginning of the pro-
cess become random quantities due to the infinite num-
ber of “contacts” with the thermostat walls.
5. Bogoliubov’s Universal Ideas and Methods
Let us start from a number of Bogoliubov’s universal
ideas and methods that penetrate all his papers in sta-
tistical mechanics and quantum theory.
The first of these ideas is Bogoliubov’s proposal to
consider the problems of many-body quantum theory
and quantum field theory on the same footing. He as-
sociated the similarity of these problems with the fact
that, in both theories (owing to the pivotal role of the
thermostat and vacuum, respectively), one has to deal
with systems of infinite number of degrees of freedom.
To realize this approach, Bogoliubov consistently used
the second quantization method. A brief version of this
method was published in the monograph “Lectures on
Quantum Statistics” in 1949.
Prior to Bogoliubov’s works, the second quantization
method was thought to be a sophisticated technical trick.
He succeeded in uncovering the deep physical meaning
of this method, and giving the notion of “quasiparticle”
its modern status. Moreover, he began to consistently
apply this method not only to wave functions but also
to dynamic variables, which allowed him to establish its
deep relation to his method of statistical operators of
groups of molecules. Finally, for the first time in the
world literature, Bogoliubov showed the way of formulat-
ing a classical analog of the second quantization method.
In particular, he used this method to derive microscopic
solutions to the Vlasov and Boltzmann–Enskog kinetic
equations.
Another universal idea put forward in his 1946 report,
concerns a specific canonical transformation, since then
called the Bogoliubov (u, v)-transformation. This trans-
formation itself forms the basis of his microscopic theory
of superfluidity of Bose and Fermi systems. However, the
physical importance of this seemingly pure mathemati-
cal method is much deeper.
Quite a new situation appears in systems with an infi-
nite number of degrees of freedom. Remaining canonical,
the transformation of the same form leads to a unitary-
nonequivalent representation of commutation relations.
ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 1 145
O.N. GOLUBJEVA, L.L. JENKOVSZKY, A.D. SUKHANOV
In this case, qualitatively different “vacua” correspond
to initial particles and quasiparticles resulting from the
(u, v)-transformation. In other words, in this type of sys-
tems, one can observe a degeneration of the ground state
manifested in many problems, both in the quantum the-
ory of condensed matter and quantum field theory, and
even in models of the early Universe.
The next step in the development of the integral ap-
proach to the solution of classical and quantum prob-
lems was made by Bogoliubov in April 1954 when he
presented the important report: “Equations with varia-
tional derivatives in problems of statistical physics and
quantum field theory”.
In that report, he proposed a presumptive view of the
method of equations in variational derivatives, closely
related to the second quantization method. Due to
this interconnection, it proved to be effective both in
many-body quantum theory and in quantum field the-
ory. The author was emphasizing that the “efficiency
of the method is related to the presence of an infinitely
large group of particles (either real or virtual) rather
than to dynamical systems being quantized or classical”.
Presently, the range of applicability of this universal
idea of Bogoliubov is even wider due to the development
of the versions of quantum field theory at finite tem-
peratures, in which the vacuum and the thermostat are
now supposed to be an integral thermofield vacuum. In
fact, in this case, the quantum model of the thermostat
introduced by Bogoliubov in 1978 is used.
6. Three Great Physics Theories
Among many outstanding scientific results in theoreti-
cal and mathematical physics, the following three great
physics theories are unique.
Bogoliubov’s kinetic theory of matter
Bogoliubov’s monograph “Problems of Dynamical The-
ory in Statistical Physics” (1946) is recognized to be
a classical work in the world scientific literature. The
book, in which, typically of Bogoliubov, formal mathe-
matics is deeply and intrinsically connected with intu-
itive physics, gained world-wide recognition. The book
enjoyed multiple editions and translations into many
languages. It largely predetermined the evolution of
nonequilibrium and equilibrium statistical mechanics in
the second half of the 20th century.
By this monograph, Bogoliubov undoubtedly marked,
after Boltzmann and Gibbs, a new era in statistical
physics. It suggested universal ideas of the weakening
of correlations, the hierarchy of relaxation times, the
abridged description of dynamical systems, the assign-
ing of a clear physical meaning to the thermodynam-
ical limiting transition. Finally, the famous chain of
Bogoliubov equations (BBGKY-hierarchy) was derived,
and the Bogoliubov–Balescu–Lenard collision integral
for charged particle systems was introduced.
In his 1946 book, from the very beginning, Bogoli-
ubov noted the fundamental contradiction inherent in
the method of obtaining the kinetic equation by Boltz-
mann. The elimination of this contradiction became a
major objective that Bogoliubov was guided by in both
the 1946 monograph and further studies.
Following this way, he was the first to make common
the equivalence of the description of classical mechanics
problems using Hamilton’s equations and the Liouville
equation. In doing so, it was shown that the use of
the Liouville equation does not distort the deterministic
character of the system if the stochastic action of the
environment is absent.
The account for this action radically changes the pat-
tern and makes it one of the main physical features of
Bogoliubov’s kinetic theory. Induced by this action (due
to the weakening of a correlation between their dynami-
cal states), the objects of the system move, for large time
intervals, practically without collisions with each other.
This means that, in the asymptotic limit, the description
of the original system of interacting particles reduces to
the description of the system of “free quasiparticles”.
One should also stress the physical differences be-
tween the kinetic equations in Boltzmann’s and Bogoli-
ubov’s theories. In Boltzmann’s theory, the hypothesis
of molecular chaos is introduced a priori, which leads to
a complete neglect of the correlations between the dy-
namical states of molecules. In addition, it is assumed
that the individual motions of molecules and the stochas-
tic process of binary collisions do not interfere with each
other. Furthermore, the universal idea of the essential
role of pair correlations underlies Bogoliubov’s theory.
Bogoliubov returned to a further elaboration of the
fundamentals of the kinetic theory in the 1970s. The
paper “Microscopic solutions of the Bolzmann–Enskog
equation in the kinetic theory of hard spheres” (1975)
is a direct continuation of the famous 1946 monograph.
The article deals with the important question of the re-
lation between the dynamic and kinetic properties of the
system. It was aimed at showing that the Boltzmann–
Enskog kinetic equation has microscopic solutions corre-
sponding to the exact motion of particles. Thereby, Bo-
goliubov’s statement that elastic collisions alone, with-
out the stochastic action of the environment, are not able
146 ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 1
NIKOLAI NIKOLAEVICH BOGOLIUBOV
to result in the stochastization of the system as a whole,
was fully confirmed.
Bogoliubov’s quantum theory of condensed
matter
Since autumn 1946, Bogoliubov started the realizatioin
of his universal approach to the description of Nature at
both micro- and macro-levels. His report “On the theory
of superfluidity” passed into history forever. This unique
paper, reissued many times in many languages, is among
the most frequently cited theoretical studies of the 20th
century. Below, we focus on its physical ideas.
Let us recall the set of Bogoliubov’s universal ideas
initiated by the famous report of 1946. First of all, one
should mention the ideas of quasiaverages and sponta-
neous symmetry breaking. First expressed in connection
with the problem of 4He superfluidity, both of these ideas
were further developed by Bogoliubov. He applied them
to various problems of statistical mechanics, including
the theories of superconductivity, ferromagnetism, crys-
talline long-range order, etc., as well as to describing
nuclear matter and properties of massive nuclei. Bo-
goliubov highly valued these ideas and devoted exten-
sive publications to them. Two of his talks dedicated
to these results, in Utrecht (1960) and Hamburg (1973),
were considered by him to be most important.
Judging by the title of Bogoliubov’s report “On some
problems of the theory of superconductivity” (1960), one
could get the impression that this paper is devoted to
a very special problem. However, it advanced a gen-
eral physical idea. As noted by the author, it was for
the first time that he clearly formulated the method of
quasiaverages, though intuitively he used it since 1946.
In this connection, Bogoliubov focused his attention
on the notion of degeneracy of a thermal equilibrium
state. He showed that the naive idea of any state being
nondegenerate was invalid, in fact. In the Nature, we
come across thermal equilibrium states that are degen-
erate in some group of symmetries, usually hidden when
using ordinary Gibbs averages.
According to Bogoliubov, for the derivation of an ad-
equate description, one should first remove degeneracy,
thus violating the invariance under transformations from
the corresponding group of symmetries. Hence, in order
“to use any form of perturbation theory for the study of
a degenerate state of statistical equilibrium, one should
first remove a degeneracy or, which is the same, use not
ordinary averages obeying all selection rules but quasi-
averages which do not obey some of them”.
As Bogoliubov said during the receipt of the
A.P. Karpinsky Prize (1981), “in the paper on quasiav-
erages, a fundamental theorem was also proved, accord-
ing to which a long-range interaction always begins in
a quantum system under spontaneous symmetry break-
ing. In other words, there appear massless excitations,
quanta of types of photons or phonons... It was found
out later on that if the theory of the so-called gauge
fields is unified with the theory of spontaneous symme-
try breaking, a set of a massless Goldstone boson and
a massless gauge boson is equivalent to a massive gauge
boson”. It is well known that this original idea of Bo-
goliubov was further developed by Higgs, who realized
it in the fundamental theory of electroweak interaction.
The appearance of “anomalous averages” of Fermi bi-
linear operators, that do not conserve the number of
particles in the theory of superconductivity, led Bogoli-
ubov to a new universal result. He showed that the gen-
eralization of the method of self-consistent field in the
many-body quantum theory made possible to account
for the pair correlations. It was named the Hartree–
Fock–Bogoliubov variational principle. In these papers,
Bogoliubov proposed also the hypothesis of superfluid-
ity of the nuclear matter that was proved by a lot of
experiments.
Finally, the most impressive among all Bogoliubov’s
universal ideas, in our opinion, exhibiting its general
physical nature, was also formulated for the first time
in his report of 1946. It is the spontaneous symmetry
breaking due to the degeneracy of the ground state. This
idea was thoroughly characterized by the author in his
talk “On spontaneous symmetry breaking in statistical
mechanics” (1973) delivered in Hamburg at the ceremony
of awarding him the Planck gold medal.
After the creation, in 1957–1958, of Bogoliubov’s su-
perconductivity theory, the idea of spontaneous symme-
try breaking went beyond the scope of statistical me-
chanics and came into use in many fields of physics.
Especially, it came into a wide use in the description
of the early stages of the evolution of the Universe.
Later on, this idea together with the Bogoliubov’s (u, v)-
transformation was applied to the quantum theory of
gauge fields, called the Higgs mechanism, which is now
an important part of the Standard Model of elementary
particles.
The importance of this Bogoliubov’s idea is even
greater. It touches upon the problem of the relation
between the properties of the Hamiltonian entering the
equations and the properties of system’s states. Spon-
taneous symmetry breaking is the most illustrative ex-
ample of this fact. At first, this phenomenon seemed to
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O.N. GOLUBJEVA, L.L. JENKOVSZKY, A.D. SUKHANOV
be merely an accident (anomaly). Nowadays, the situa-
tion has changed radically. In particular, the observation
of various artificial Bose–Einstein condensates clearly
shows the universality of the 1946 Bogoliubov theory
for weakly nonideal Bose gases. This idea is simultane-
ously extended to other branches of physics. Obviously,
it is high time to explain “spontaneous symmetry gen-
eration” under some exceptional conditions rather than
spontaneous symmetry breaking.
It is appropriate here to give a global estimate of the
1946 Bogoliubov theory. For many years, it was consid-
ered merely as an auxiliary mathematical justification of
Landau’s theory of superfluidity. In fact, Bogoliubov in
his theory made a principally new step – he predicted, for
the first time, the existence of a new state of condensed
matter in the Nature – nearly perfect fluids including the
Bose–Einstein condensates (BECs) in nonideal gases of
particles or quasiparticles. The number of newly dis-
covered BECs in condensed matter, including excitons,
magnons, etc. rapidly increases. Moreover, speculations
on a new state of matter (quark-gluon plasma) created
in high-energy heavy-ion collisions exist. Soon this may
become an indispensable element in other branches of
physics as well.
On the other hand, superfluidity and superconductiv-
ity are merely manifestations of the known properties of
the new state of matter. During the past ten years, three
Nobel prizes were assigned to the authors of theoretical
works on these problems, as well as to experimentalists
for the discovery of the BEC in dilute gases of alkali met-
als and the studies of their properties. Strange enough,
the origin of all these discoveries, Bogoliubov’s seminal
theory of 1946 was never mentioned in the press-releases
of the Nobel committee. More important for the sci-
ence is the foundation of a particular discovery. Bogoli-
ubov’s name is firmly connected to the idea of the new
condensed state of matter, and nobody will be able to
change this story.
Bogoliubov’s axiomatic quantum field theory
The next step in the development of an integral approach
to the solution of classical and quantum problems was
made by Bogoliubov in April 1954, when he presented
three important reports within only several days: “Equa-
tions with variational derivatives in problems of statis-
tical physics and quantum field theory”, “On the repre-
sentation of the Green–Schwinger functions in terms of
functional integrals”, and “Causality condition in quan-
tum field theory”.
In fact, these reports are parts of the unique work sum-
ming up Bogoliubov’s decennial meditation and stud-
ies of problems that are common for statistical physics
and quantum field theory. They formed the basis of
the famous monographs “Problems of the Theory of Dis-
persion Relations” (with B.V. Medvedev and M.K. Po-
livanov, 1956), “Introduction to the Theory of Quan-
tized Fields” (with D.V. Shirkov, 1957), “Introduction to
Axiomatic Quantum Field Theory” (with A.A. Logunov
and I.T. Todorov, 1969), “Some Aspects of Polaron The-
ory” (1981) and “Introduction to Quantum Statistical
Mechanics” (1982) (both with N.N. Bogoliubov, jr.)
It is well established that it was the unification of the
ideas of the reports that led Bogoliubov to the formula-
tion of a system of axioms that allowed him to construct
the relativistic quantum field theory based on general
principles of covariance, unitarity, and microcausality
without the direct use of the Hamilton formalism.
Moreover, his most general version of axiomatics pre-
ceded a much narrower axiomatic schemes proposed by
Lehmann, Symanzik, and Zimmermann and Wightman,
respectively. The modern Bogoliubov formulation of the
system of axioms and its inherent possibilities for the
consideration of a wider class of local models of quan-
tum field theory were revealed by Bogoliubov’s disciples
and followers in their works. The main results in this
field were later accumulated in the fundamental mono-
graph “General Principles of Quantum Field Theory”
written by Bogoliubov with A.A. Logunov, A.I. Oksak,
and I.T. Todorov (1987).
Furthermore, within his version of axiomatics, Bogoli-
ubov was the first to prove dispersion relations for the
pion-nucleon scattering. The initial postulates and the
results he obtained in this field were presented by Bo-
goliubov and Vladimirov in their contributions “On some
mathematical problems of quantum field theory” to the
International Congress of Mathematicians (Edinburgh,
1958), subject of numerous discussions.
The importance of these results for theoretical physics
was also admitted by outstanding researchers. Seri-
ous interest in these investigations is demonstrated by
the fact that, after the International Congress on The-
oretical Physics (Seattle, 1956), where Bogoliubov re-
ported, for the first time, on this subject, the contents
of the future monograph was twice published in English
and was widely covered abroad. Shortly thereafter, Bo-
goliubov showed the versatility of the method of dis-
persion relations in both quantum field theory (“The
method of dispersion relations and perturbation the-
ory” (1959, with A.A. Logunov and D.V. Shirkov) and
almost simultaneously in statistical physics (“Retarded
148 ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 1
NIKOLAI NIKOLAEVICH BOGOLIUBOV
and advanced Green functions in statistical physics”
(1959, with S.V. Tyablikov). These two papers became
very popular and have many applications in further stu-
dies.
Among Bogoliubov’s encyclopedic results which
formed a whole line of investigations in quantum field
theory, it is worth noting, undoubtedly, the discov-
ery of renormalization group theory as an exact prop-
erty of a renormalized quantum-field solution to Green
functions. It culminated in the construction (1955,
with A.A. Logunov and D.V. Shirkov) of the renormal-
ization group method (RGM) with numerous applica-
tions in many fields of theoretical and mathematical
physics.
The most important point of these works was the idea
of invariant electron charge and a more general notion
of invariant (running) coupling constant. The latter was
used in the concept of asymptotic freedom that con-
tributed to the advances of the non-Abelian gauge field
theory and to the convergence of numerical values for
three invariant coupling functions typical of the theories
of “grand unification” of interactions.
Two ideas of Bogoliubov are among the most impor-
tant achievements of the elementary particles theory,
namely the existence of colored quarks and the model
of quasiindependent quarks. Bogoliubov (1965, in col-
laboration with B.V. Struminsky and A.N. Tavkhelidze)
were the first who suggested to introduce a new quan-
tum number! Later on, it was called color. Their
model of quasiindependent quarks was used as the
concept of asymptotic freedom that led to the con-
struction of quantum chromodynamics and was applied
to the theories of “grand unification” of all interac-
tions.
7. All-Time Man
To conclude, we cite a fragment from Bogoliubov’s ple-
nary report “Mathematical problems of quantum field
theory and quantum statistics” at the 1-st International
Conference on Theoretical and Mathematical Physics
(1972, Moscow): “In the last 20–25 years, a new field of
research emerged – the modern theoretical and mathe-
matical physics as an integral science occupying an inter-
mediate position between theoretical physics and math-
ematics. This line of investigations is called into be-
ing, first of all, by new tasks of the quantum physics
of systems with an infinite number of degrees of free-
dom, nonrelativistic and relativistic, and requires the
involvement of modern powerful mathematical tools...”.
Since then, this point of view gained a wide recogni-
tion.
It was a noble mission of Bogoliubov to become one
of the founders of this field of research – theoretical and
mathematical physics as an integral science and thus to
lay a landmark in the foundation of the universal ther-
mal quantum field theory of the matter surrounding us.
As time passes by, the field of applications of his ideas
becomes even wider.
Although the recognition of the scientific achievements
came to Nikolai Nikolaevich rather early, it is not yet
complete. The majority of his fundamental ideas were
ahead of the time they appeared, for which reason they
did not receive the due understanding and appreciation.
The publication of the 12-volume edition of his works in
Russia (2005–2009) reveals a rich intellectual treasure,
whose comprehension will be the task of the next gener-
ation of researchers.
Implementing the will of the teacher, his disciples, be-
ing specialists in specific fields of science, continue de-
veloping his universal ideas tending to integrity in the
description of the Nature. In other words, these fields
are fundamentally indivisible in the works of the Master,
as they are in the Nature. Consequently, even a cur-
sory acquaintance with Bogoliubov’s fundamental ideas
shows how rich his scientific heritage is and also the
general way his disciples and followers should develop
his ideas, in the spirit of Leibniz and Planck, in the fu-
ture.
There are few names in the history of sciences that
deserve to be qualified as Great. Good reasons should
be for that. Primary is, or course, the scale of their
scientific achievements. Next is the value of a relevant
contribution to the universal culture.
Bogoliubov’s performance as that of a scientist, whose
main ideas become classical already during his life, con-
firm beyond any doubt the validity of his position among
the leaders of the exact sciences of the XXth century.
However, this is not the whole story of the great man.
Everybody who knew Bogoliubov personally bears in his
mind his sublime faith in the spirit and the intellect of
the human beings.
All his life was a testimony of these qualities. He
made no secret of his devotion to the Christian val-
ues (he was attending the Orthodox church, was ac-
tively promoting the reconstruction of temples, etc.), re-
specting other confessions at the same time, and was
against any religion hostility. He was a profound con-
noisseur of literature, philosophy, ancient history, and
history of religions, with special admiration for the Me-
dieval philosophers, whose religious teaching was, for
ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 1 149
O.N. GOLUBJEVA, L.L. JENKOVSZKY, A.D. SUKHANOV
him, an expression of deep mathematical conception of
the world.
As a theoretical physicist, participated in the Russian
atomic project, he did his best to avoid the catastrophic
consequences of the possession of the atomic power. He
was active in the Pagwash peace movement and sup-
ported, with all his force, the radiobiological studies and
their medical applications, in particular those in oncol-
ogy. He was cut to the heart by the Chernobyl’ disas-
ter not only because it concerned Russia and Ukraine,
two countries he considered his motherlands. More-
over, he was concerned about the threat to the whole
mankind.
Bogoliubov was a humanist in the true sublime sense
of this word. He was a man who, like the Renaissance
Titans, unified the fundamental scientific and spiritual
values in his creativity.
The work of O. Golubjeva and A. Sukhanov was sup-
ported by RFBR (Project 07-06-00239a).
1. Nikolai Nikolaevich Bogoliubov, Collection of Scientific
Works in Twelve Volumes, Ed.-in-Chief A.D. Sukhanov
(Nauka, Moscow, 2005–2009) (in Russian).
2. A.N. Bogoliubov, N.N. Bogoliubov, Life and Scientific
Work, edited by V.G. Kadyshevsky (JINR, Dubna, 1996)
(in Russian).
Received 29.10.09
МИКОЛА МИКОЛАЙОВИЧ БОГОЛЮБОВ –
НАЙВИДАТНIШИЙ ВЧЕНИЙ I ГУМАНIСТ
XX-ГО СТОЛIТТЯ
О.Н. Голубєва, Л.Л. Єнковський, О.Д. Суханов
Р е з ю м е
21 серпня 2009 року вiдзначалося столiття вiд дня народження
Миколи Миколайовича Боголюбова – класика свiтової науки.
Iм’я Боголюбова назавжди увiйшло в iсторiю цивiлiзацiї. Вiн
був вченим енциклопедичного масштабу, одним з творцiв су-
часної теоретичної i математичної фiзики, засновником сузiр’я
наукових шкiл, а також широко вiдомого журналу “Теоретична
i математична фiзика”. Логотип Ф∩М, запропонований ним,
став знаком серiї мiжнародних конгресiв з математичної фi-
зики (останнiй, XVI-й Конгрес цiєї серiї вiдбувся у Празi 3–8
серпня 2009 року).
Ця стаття є коротким оглядом основних наукових результа-
тiв М.М. Боголюбова. Оригiнальнi роботи М.М. Боголюбова,
якi згадуються в оглядi, можна знайти в його збiрцi творiв [1],
а коротку бiографiю – в роботi [2].
150 ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 1
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