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Felix Berezin
Felix Alexandrovich Berezin (russian: Фе́ликс Алекса́ндрович Бере́зин; 25 April 1931 – 14 July 1980) was a Soviet Russian mathematician and physicist known for his contributions to the theory of supersymmetry and supermanifolds as well as to the path integral formulation of quantum field theory. Berezin studied at the Moscow State University, but was not allowed to do his graduate studies there on account of his Jewish origin (his mother was Jewish). For the next three years Berezin taught at Moscow high schools. He continued to study mathematical physics under direction of Israel Gelfand. After Khrushchev's liberalization, he joined the Department of Mathematics at the Moscow State University at the age of 25. The Berezin integral over anticommuting Grassmann variables is named for him, as is the closely related construction of the Berezinian which may be regarded as the " super"-analog of the determinant. Berezin drowned during a summer trip i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow
Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million residents within the city limits, over 17 million residents in the urban area, and over 21.5 million residents in the metropolitan area. The city covers an area of , while the urban area covers , and the metropolitan area covers over . Moscow is among the world's largest cities; being the most populous city entirely in Europe, the largest urban and metropolitan area in Europe, and the largest city by land area on the European continent. First documented in 1147, Moscow grew to become a prosperous and powerful city that served as the capital of the Grand Duchy that bears its name. When the Grand Duchy of Moscow evolved into the Tsardom of Russia, Moscow remained the political and economic center for most of the Tsardom's history. When th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supersymmetry
In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories exist. Supersymmetry is a spacetime symmetry between two basic classes of particles: bosons, which have an integer-valued spin and follow Bose–Einstein statistics, and fermions, which have a half-integer-valued spin and follow Fermi–Dirac statistics. In supersymmetry, each particle from one class would have an associated particle in the other, known as its superpartner, the spin of which differs by a half-integer. For example, if the electron exists in a supersymmetric theory, then there would be a particle called a ''"selectron"'' (superpartner electron), a bosonic partner of the electron. In the simplest supersymmetry theories, with perfectly " unbroken" supersymmetry, each pair of superpartners would share the same mass and intern ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roland Dobrushin
Roland Lvovich Dobrushin (russian: Рола́нд Льво́вич Добру́шин) (July 20, 1929 – November 12, 1995) was a mathematician who made important contributions to probability theory, mathematical physics, and information theory. Life and work Dobrushin received his Ph.D. at Moscow State University under the supervision of Andrey Kolmogorov. In statistical mechanics, he introduced (simultaneously with Lanford and Ruelle) the DLR equations for the Gibbs measure. Together with Kotecký and Shlosman, he studied the formation of droplets in Ising-type models, providing mathematical justification of the Wulff construction. He was a foreign member of the American Academy of Arts and Sciences, Academia Europæa and US National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nikolay Bogolyubov
Nikolay Nikolayevich Bogolyubov (russian: Никола́й Никола́евич Боголю́бов; 21 August 1909 – 13 February 1992), also transliterated as Bogoliubov and Bogolubov, was a Soviet and Russian mathematician and theoretical physicist known for a significant contribution to quantum field theory, classical and quantum statistical mechanics, and the theory of dynamical systems; he was the recipient of the 1992 Dirac Medal. Biography Early life (1909–1921) Nikolay Bogolyubov was born on 21 August 1909 in Nizhny Novgorod, Russian Empire to Russian Orthodox Church priest and seminary teacher of theology, psychology and philosophy Nikolay Mikhaylovich Bogolyubov, and Olga Nikolayevna Bogolyubova, a teacher of music. The Bogolyubovs relocated to the village of Velikaya Krucha in the Poltava Governorate (now in Poltava Oblast, Ukraine) in 1919, where the young Nikolay Bogolyubov began to study physics and mathematics. The family soon moved to Kiev in 1921, where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soviet Physics Uspekhi
''Physics-Uspekhi'' is a peer-reviewed scientific journal. It is an English translation of the Russian journal of physics, ''Uspekhi Fizicheskikh Nauk'' (russian: Успехи физических наук, ''Advances in Physical Sciences'') which was established in 1918. The journal publishes long review papers which are intended to generalize and summarize previously published results, making them easier to use and to understand. The journal covers all topics of modern physics. The English version has existed since 1958, first under the name ''Soviet Physics Uspekhi'' and after 1993 as ''Physics-Uspekhi''. The year 2008 marked the 90th birthday with a jubilee retrospective. The founder of the journal, Eduard Shpolsky, was editor-in-chief from 1918 to his death in 1975. Vitaly Ginzburg, connected with the journal since before World War II, was appointed editor-in-chief in 1998. In his 2006 Nobel autobiography, Ginzburg called it "a good and useful journal" and credited its "mainte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sergei Novikov (mathematician)
Sergei Petrovich Novikov (also Serguei) (Russian: Серге́й Петро́вич Но́виков) (born 20 March 1938) is a Soviet and Russian mathematician, noted for work in both algebraic topology and soliton theory. In 1970, he won the Fields Medal. Early life Novikov was born on 20 March 1938 in Gorky, Soviet Union (now Nizhny Novgorod, Russia). He grew up in a family of talented mathematicians. His father was Pyotr Sergeyevich Novikov, who gave a negative solution to the word problem for groups. His mother, Lyudmila Vsevolodovna Keldysh, and maternal uncle, Mstislav Vsevolodovich Keldysh, were also important mathematicians. In 1955 Novikov entered Moscow State University, from which he graduated in 1960. Four years later he received the Moscow Mathematical Society Award for young mathematicians. In the same year he defended a dissertation for the ''Candidate of Science in Physics and Mathematics'' degree (equivalent to the PhD) at Moscow State University. In 196 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yuri Manin
Yuri Ivanovich Manin (russian: Ю́рий Ива́нович Ма́нин; born 16 February 1937) is a Russian mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logic to theoretical physics. Moreover, Manin was one of the first to propose the idea of a quantum computer in 1980 with his book ''Computable and Uncomputable''. Life and career Manin gained a doctorate in 1960 at the Steklov Mathematics Institute as a student of Igor Shafarevich. He is now a Professor at the Max-Planck-Institut für Mathematik in Bonn, and a professor emeritus at Northwestern University. Manin's early work included papers on the arithmetic and formal groups of abelian varieties, the Mordell conjecture in the function field case, and algebraic differential equations. The Gauss–Manin connection is a basic ingredient of the study of cohomology in families of algebraic varieties. He wrote a book on cubic surfaces and cubic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oscillator Representation
In mathematics, the oscillator representation is a projective unitary representation of the symplectic group, first investigated by Irving Segal, David Shale, and André Weil. A natural extension of the representation leads to a semigroup of contraction operators, introduced as the oscillator semigroup by Roger Howe in 1988. The semigroup had previously been studied by other mathematicians and physicists, most notably Felix Berezin in the 1960s. The simplest example in one dimension is given by SU(1,1). It acts as Möbius transformations on the extended complex plane, leaving the unit circle invariant. In that case the oscillator representation is a unitary representation of a double cover of SU(1,1) and the oscillator semigroup corresponds to a representation by contraction operators of the semigroup in SL(2,C) corresponding to Möbius transformations that take the unit disk into itself. The contraction operators, determined only up to a sign, have kernels that are Gaussian ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Second Quantization
Second quantization, also referred to as occupation number representation, is a formalism used to describe and analyze quantum many-body systems. In quantum field theory, it is known as canonical quantization, in which the fields (typically as the wave functions of matter) are thought of as field operators, in a manner similar to how the physical quantities (position, momentum, etc.) are thought of as operators in first quantization. The key ideas of this method were introduced in 1927 by Paul Dirac, and were later developed, most notably, by Pascual Jordan and Vladimir Fock. In this approach, the quantum many-body states are represented in the Fock state basis, which are constructed by filling up each single-particle state with a certain number of identical particles. The second quantization formalism introduces the creation and annihilation operators to construct and handle the Fock states, providing useful tools to the study of the quantum many-body theory. Quantum many-body ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Determinant
In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. It characterizes some properties of the matrix and the linear map represented by the matrix. In particular, the determinant is nonzero if and only if the matrix is invertible and the linear map represented by the matrix is an isomorphism. The determinant of a product of matrices is the product of their determinants (the preceding property is a corollary of this one). The determinant of a matrix is denoted , , or . The determinant of a matrix is :\begin a & b\\c & d \end=ad-bc, and the determinant of a matrix is : \begin a & b & c \\ d & e & f \\ g & h & i \end= aei + bfg + cdh - ceg - bdi - afh. The determinant of a matrix can be defined in several equivalent ways. Leibniz formula expresses the determinant as a sum of signed products of matrix entries such that each summand is the product of different entries, and the number of these summands is n!, the factorial of (t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grassmann Variable
In mathematical physics, a Grassmann number, named after Hermann Grassmann (also called an anticommuting number or supernumber), is an element of the exterior algebra over the complex numbers. The special case of a 1-dimensional algebra is known as a dual number. Grassmann numbers saw an early use in physics to express a path integral representation for fermionic fields, although they are now widely used as a foundation for superspace, on which supersymmetry is constructed. Informal discussion Grassmann numbers are generated by anti-commuting elements or objects. The idea of anti-commuting objects arises in multiple areas of mathematics: they are typically seen in differential geometry, where the differential forms are anti-commuting. Differential forms are normally defined in terms of derivatives on a manifold; however, one can contemplate the situation where one "forgets" or "ignores" the existence of any underlying manifold, and "forgets" or "ignores" that the forms were defined ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nikita Khrushchev
Nikita Sergeyevich Khrushchev (– 11 September 1971) was the First Secretary of the Communist Party of the Soviet Union from 1953 to 1964 and chairman of the country's Council of Ministers from 1958 to 1964. During his rule, Khrushchev stunned the communist world with his denunciation of his predecessor Joseph Stalin's crimes, and embarked on a policy of de-Stalinization with his key ally Anastas Mikoyan. He sponsored the early Soviet space program, and enactment of moderate reforms in domestic policy. After some false starts, and a narrowly avoided nuclear war over Cuba, he conducted successful negotiations with the United States to reduce Cold War tensions. In 1964, the Kremlin leadership stripped him of power, replacing him with Leonid Brezhnev as First Secretary and Alexei Kosygin as Premier. Khrushchev was born in 1894 in a village in western Russia. He was employed as a metal worker during his youth, and he was a political commissar during the Russian Civil Wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
