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Faddeev
Ludvig Dmitrievich Faddeev (also ''Ludwig Dmitriyevich''; ; 23 March 1934 – 26 February 2017) was a Soviet and Russian mathematical physicist. He is known for the discovery of the Faddeev equations in the quantum-mechanical three-body problem and for the development of path-integral methods in the quantization of non-abelian gauge field theories, including the introduction of the Faddeev–Popov ghosts (with Victor Popov). He led the Leningrad School, in which he along with many of his students developed the quantum inverse scattering method for studying quantum integrable systems in one space and one time dimension. This work led to the invention of quantum groups by Drinfeld and Jimbo. Biography Faddeev was born in Leningrad to a family of mathematicians. His father, Dmitry Faddeev, was a well-known algebraist, professor of Leningrad University and member of the Russian Academy of Sciences. His mother, Vera Faddeeva, was known for her work in numerical linear al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Faddeev–Popov Ghost
In physics, Faddeev–Popov ghosts (also called Faddeev–Popov gauge ghosts or Faddeev–Popov ghost fields) are extraneous fields which are introduced into gauge quantum field theories to maintain the consistency of the path integral formulation. They are named after Ludvig Faddeev and Victor Popov. A more general meaning of the word "ghost" in theoretical physics is discussed in Ghost (physics). Overcounting in Feynman path integrals The necessity for Faddeev–Popov ghosts follows from the requirement that quantum field theories yield unambiguous, non-singular solutions. This is not possible in the path integral formulation when a gauge symmetry is present since there is no procedure for selecting among physically equivalent solutions related by gauge transformation. The path integrals overcount field configurations corresponding to the same physical state; the measure of the path integrals contains a factor which does not allow obtaining various results directly ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leon Takhtajan
Leon Armenovich Takhtajan (; , born 1 October 1950, Yerevan) is a Russian (and formerly Soviet) mathematical physicist of Armenian descent, currently a professor of mathematics at the Stony Brook University, Stony Brook, NY, and a leading researcher at the Euler International Mathematical Institute, Saint Petersburg, Russia. Biography Leon Armenovich Takhtajan was born in Yerevan, Soviet Union, in 1950, son of the Armenian Russian botanist Armen Takhtajan. Education Takhtajan received in 1975 his Ph.D. (Russian candidate degree) from the Steklov Institute (Leningrad Department) under Ludvig Faddeev with thesis ''Complete Integrability of the Equation u_-u_+\sin (u)=0''. He was then employed at the Steklov Institute (Leningrad Department) and in 1982 received his D.S. degree (doctor of science, 2nd degree in Russia) with thesis ''Completely integrable models of field theory and statistical mechanics''. Career Since 1992 he has been a professor at Stony Brook University wher ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Dilogarithm
In mathematics, the quantum dilogarithm is a special function defined by the formula : \phi(x)\equiv(x;q)_\infty=\prod_^\infty (1-xq^n),\quad , q, 0. References * * * * * * * External links * {{nlab, id=quantum+dilogarithm, title=quantum dilogarithm Special functions Q-analogs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Faddeev Equations
The Faddeev equations, named after their discoverer Ludvig Faddeev, describe, at once, all the possible exchanges/ interactions in a system of three particles in a fully quantum mechanical formulation. They can be solved iteratively. In general, Faddeev equations need as input a potential that describes the interaction between two individual particles. It is also possible to introduce a term in the equation in order to take also three-body forces into account. The Faddeev equations are the most often used non-perturbative formulations of the quantum-mechanical three-body problem. Unlike the three body problem in classical mechanics, the quantum three body problem is uniformly soluble. In nuclear physics, the off the energy shell nucleon-nucleon interaction has been studied by analyzing (n,2n) and (p,2p) reactions on deuterium targets, using the Faddeev Equations. The nucleon-nucleon interaction is expanded (approximated) as a series of separable potentials. The Coulomb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dirac Medal (ICTP)
The Dirac Medal of the ICTP is given each year by the International Centre for Theoretical Physics (ICTP) in honour of physicist Paul Dirac. The award, announced each year on 8 August (Dirac's birthday), was first awarded in 1985. An international committee of distinguished scientists selects the winners from a list of nominated candidates. The Committee invites nominations from scientists working in the fields of theoretical physics or mathematics. The Dirac Medal of the ICTP is not awarded to Nobel Laureates, Fields Medalists, or Wolf Prize winners. However, several Dirac Medallists have subsequently won one of these awards. The medallists receive a prize of US$5,000. Recipients See also * List of physics awards * List of awards named after people This is a list of awards that are named after people. A B C D E F G H I J K L M N O P R S T U–V W Y Z See also *Lists of awards *List of eponyms *List of awards na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shaw Prize
The Shaw Prize is a set of three annual awards presented by the Shaw Prize Foundation in the fields of astronomy, medicine and life sciences, and mathematical sciences. Established in 2002 in Hong Kong, by Hong Kong entertainment mogul and philanthropist Run Run Shaw (邵逸夫), the awards honour "individuals who are currently active in their respective fields and who have recently achieved distinguished and significant advances, who have made outstanding contributions in academic and scientific research or applications, or who in other domains have achieved excellence." The prize has been described as the "Nobel of the East". Award The prize consists of three awards in the fields of astronomy, life science and medicine, and mathematical sciences; it is not awarded posthumously. Nominations are submitted by invited individuals beginning each year in September. Winners are announced in the summer and receive the award at a ceremony in early autumn. Each award consists of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Inverse Scattering Method
In quantum physics, the quantum inverse scattering method (QISM), similar to the closely related algebraic Bethe ansatz, is a method for solving integrable models in 1+1 dimensions, introduced by Leon Takhtajan and L. D. Faddeev in 1979. It can be viewed as a quantized version of the classical inverse scattering method pioneered by Norman Zabusky and Martin Kruskal used to investigate the Korteweg–de Vries equation and later other integrable partial differential equations. In both, a Lax matrix features heavily and scattering data is used to construct solutions to the original system. While the classical inverse scattering method is used to solve integrable partial differential equations which model continuous media (for example, the KdV equation models shallow water waves), the QISM is used to solve many-body quantum systems, sometimes known as spin chains, of which the Heisenberg spin chain is the best-studied and most famous example. These are typically discrete sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Samson Shatashvili
Samson Lulievich Shatashvili ( ka, სამსონ შათაშვილი; Russian: Самсон Лулиевич Шаташвили, born February 1960) is a theoretical and mathematical physicist who has been working at Trinity College, Dublin, Trinity College Dublin, Ireland, since 2002. He holds the Trinity College Dublin Chair of Natural Philosophy and is the director of the Hamilton Mathematics Institute. He is also affiliated with the Institut des Hautes Études Scientifiques (IHÉS), where he held the Louis Michel Chair from 2003 to 2013 and the Israel Gelfand Chair from 2014 to 2019. Prior to moving to Trinity College, he was a professor of physics at Yale University from 1994. Background Shatashvili received his PhD in 1984 at the St. Petersburg Department of Steklov Institute of Mathematics of Russian Academy of Sciences, Steklov Institute of Mathematics in Saint Petersburg under the supervision of Ludvig Faddeev, Ludwig Faddeev (and Vladimir Korepin). The top ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Evgeny Sklyanin
Evgeny Konstantinovich Sklyanin (, born May 24, 1955, in Leningrad, Soviet Union) is a mathematical physicist, currently a professor of mathematics at the University of York. His research is in the fields of integrable systems and quantum groups. His major contributions are in the theory of quantum integrable systems, separation of variables, special functions. Biography He graduated from the Department of Physics, Leningrad State University (USSR) in 1978 and earned PhD (Candidate) in 1980 and DrSci (Habilitation) degree in 1989, both at Steklov Mathematical Institute, St. Petersburg. He then held various research positions at Steklov until 2001, when he moved to the University of York. He provided, via particular examples, ideas that led to the discovery of quantum groups and Yangians. He pioneered the investigation of quantum integrable systems with boundaries. He developed the method of separation of variables in the theory of integrable systems. He was elected Fellow of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vladimir Korepin
Vladimir E. Korepin (born 1951) is a professor at the C. N. Yang Institute of Theoretical Physics of the Stony Brook University. Korepin made research contributions in several areas of mathematics and physics. Educational background Korepin completed his undergraduate study at Saint Petersburg State University, graduating with a diploma in theoretical physics in 1974. In that same year he was employed by the Mathematical Institute of Academy of Sciences. He worked there until 1989, obtaining his PhD in 1977 under the supervision of Ludwig Faddeev. At the same institution he completed his postdoctoral studies. In 1985, he received a Doctor of Science degree in mathematical physics. Contributions to physics Korepin has made contributions to several fields of theoretical physics. Although he is best known for his involvement in condensed matter physics and mathematical physics, he significantly contributed to quantum gravity as well. In recent years, his work has focused on aspe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yangian
In representation theory, a Yangian is an infinite-dimensional Hopf algebra, a type of a quantum group. Yangians first appeared in physics in the work of Ludvig Faddeev and his school in the late 1970s and early 1980s concerning the quantum inverse scattering method. The name ''Yangian'' was introduced by Vladimir Drinfeld in 1985 in honor of C.N. Yang. Initially, they were considered a convenient tool to generate the solutions of the quantum Yang–Baxter equation. The center of the Yangian can be described by the quantum determinant. The Yangian is a degeneration of the quantum loop algebra (i.e. the quantum affine algebra at vanishing central charge). Description For any finite-dimensional semisimple Lie algebra ''a'', Drinfeld defined an infinite-dimensional Hopf algebra ''Y''(''a''), called the Yangian of ''a''. This Hopf algebra is a deformation of the universal enveloping algebra ''U''(''a'' 'z'' of the Lie algebra of polynomial loops of ''a'' given by explicit generat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Physics
Mathematical physics is the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". An alternative definition would also include those mathematics that are inspired by physics, known as physical mathematics. Scope There are several distinct branches of mathematical physics, and these roughly correspond to particular historical parts of our world. Classical mechanics Applying the techniques of mathematical physics to classical mechanics typically involves the rigorous, abstract, and advanced reformulation of Newtonian mechanics in terms of Lagrangian mechanics and Hamiltonian mechanics (including both approaches in the presence of constraints). Both formulations are embodied in analytical mechanics and lead ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
