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Chiral Model
In nuclear physics, the chiral model, introduced by Feza Gürsey in 1960, is a phenomenological model describing effective interactions of mesons in the chiral limit (where the masses of the quarks go to zero), but without necessarily mentioning quarks at all. It is a nonlinear sigma model with the principal homogeneous space of a Lie group G as its target manifold. When the model was originally introduced, this Lie group was the SU(''N''), where ''N'' is the number of quark flavors. The Riemannian metric of the target manifold is given by a positive constant multiplied by the Killing form acting upon the Maurer–Cartan form of SU(''N''). The internal global symmetry of this model is G_L \times G_R, the left and right copies, respectively; where the left copy acts as the left action upon the target space, and the right copy acts as the right action. Phenomenologically, the left copy represents flavor rotations among the left-handed quarks, while the right copy describes ro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integrable Chiral Model Soliton Scattering
In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first integrals, that its motion is confined to a submanifold of much smaller dimensionality than that of its phase space. Three features are often referred to as characterizing integrable systems: * the existence of a ''maximal'' set of conserved quantities (the usual defining property of complete integrability) * the existence of algebraic invariants, having a basis in algebraic geometry (a property known sometimes as algebraic integrability) * the explicit determination of solutions in an explicit functional form (not an intrinsic property, but something often referred to as solvability) Integrable systems may be seen as very different in qualitative character from more ''generic'' dynamical systems, which are more typically chaotic systems ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Global Symmetry
The symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation. A family of particular transformations may be ''continuous'' (such as rotation of a circle) or ''discrete'' (e.g., reflection of a bilaterally symmetric figure, or rotation of a regular polygon). Continuous and discrete transformations give rise to corresponding types of symmetries. Continuous symmetries can be described by Lie groups while discrete symmetries are described by finite groups (see ''Symmetry group''). These two concepts, Lie and finite groups, are the foundation for the fundamental theories of modern physics. Symmetries are frequently amenable to mathematical formulations such as group representations and can, in addition, be exploited to simplify many problems. Arguably the most important example of a symmetry in physics is that the speed of light has the same value in all frames of re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chiral Perturbation Theory
Chiral perturbation theory (ChPT) is an effective field theory constructed with a Lagrangian (field theory), Lagrangian consistent with the (approximate) chiral symmetry of quantum chromodynamics (QCD), as well as the other symmetries of parity (physics), parity and charge conjugation.Heinrich Leutwyler (2012), Chiral perturbation theory Scholarpedia, 7(10):8708. ChPT is a theory which allows one to study the low-energy dynamics of QCD on the basis of this underlying chiral symmetry. Goals In the theory of the strong interaction of the Standard Model, standard model, we describe the interactions between quarks and gluons. Due to the running of the strong coupling constant, we can apply perturbation theory in the coupling constant only at high energies. But in the ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skyrmion
In particle theory, the skyrmion () is a topologically stable field configuration of a certain class of non-linear sigma models. It was originally proposed as a model of the nucleon by (and named after) Tony Skyrme in 1961. As a topological soliton in the pion field theory (physics), field, it has the remarkable property of being able to model, with reasonable accuracy, multiple low-energy properties of the nucleon, simply by fixing the nucleon radius. It has since found application in solid-state physics, as well as having ties to certain areas of string theory. Skyrmions as topological objects are important in solid-state physics, especially in the emerging technology of spintronics. A two-dimensional magnetic skyrmion, as a topological object, is formed, e.g., from a 3D effective-spin "hedgehog" (in the field of micromagnetics: out of a so-called "Bloch sphere, Bloch point" singularity of homotopy degree +1) by a stereographic projection, whereby the positive north-pole spin is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Soliton
In mathematics and physics, solitons, topological solitons and topological defects are three closely related ideas, all of which signify structures in a physical system that are stable against perturbations. Solitons do not decay, dissipate, disperse or evaporate in the way that ordinary waves (or solutions or structures) might. The stability arises from an obstruction to the decay, which is explained by having the soliton belong to a different topological homotopy class or cohomology class than the base physical system. More simply: it is not possible to continuously transform the system with a soliton in it, to one without it. The mathematics behind topological stability is both deep and broad, and a vast variety of systems possessing topological stability have been described. This makes categorization somewhat difficult. Overview The original soliton was observed in the 19th century, as a solitary water wave in a barge canal. It was eventually explained by noting that the K ... [...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] |
Quantum Group
In mathematics and theoretical physics, the term quantum group denotes one of a few different kinds of noncommutative algebras with additional structure. These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebras), compact matrix quantum groups (which are structures on unital separable C*-algebras), and bicrossproduct quantum groups. Despite their name, they do not themselves have a natural group structure, though they are in some sense 'close' to a group. The term "quantum group" first appeared in the theory of quantum integrable systems, which was then formalized by Vladimir Drinfeld and Michio Jimbo as a particular class of Hopf algebra. The same term is also used for other Hopf algebras that deform or are close to classical Lie groups or Lie algebras, such as a "bicrossproduct" class of quantum groups introduced by Shahn Majid a little after the work of Drinfeld and Jimbo. In Drinfeld's approach, quantum groups arise as Hopf algebras depe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lax Pair
A lax is a salmon. LAX as an acronym most commonly refers to Los Angeles International Airport in Southern California, United States. LAX or Lax may also refer to: Places Within Los Angeles * Union Station (Los Angeles), Los Angeles' main train depot, whose Amtrak station code is "LAX" * The Port of Los Angeles, whose port identifier code is "LAX" Other * Lax, Switzerland, a municipality of the canton of Valais * Lax Lake (other) * La Crosse, Wisconsin, a city on the Mississippi River Sports * Los Angeles Xtreme, a former American football team * Lacrosse, a sport * The Latin American Xchange, a professional wrestling stable Media and entertainment * ''LAX'' (album), the third studio album from rapper The Game * ''LAX'' (TV series), a 2004–05 television series set in Los Angeles International Airport * " LA X", the two-part sixth season 2010 premiere of the television show ''Lost'' * LAX, a night club at Luxor Las Vegas * "LAX", a song by the rapper X ... [...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] |
Nicolai Reshetikhin
Nicolai Yuryevich Reshetikhin (, born October 10, 1958, in Leningrad, Soviet Union) is a mathematical physicist, currently a professor of mathematics at Tsinghua University, China and a professor of mathematical physics at the University of Amsterdam (Korteweg-de Vries Institute for Mathematics). He is also a professor emeritus at the University of California, Berkeley. His research is in the fields of low-dimensional topology, representation theory, and quantum groups. His major contributions are in the theory of quantum integrable systems, in representation theory of quantum groups and in quantum topology. He and Vladimir Turaev constructed invariants of 3-manifolds which are expected to describe quantum Chern–Simons field theory introduced by Edward Witten. He earned his bachelor's degree and master's degree from Leningrad State University in 1982, and his Ph.D. from the Steklov Mathematical Institute in 1984. He gave a plenary lecture at the International Congress of Mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ludwig 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 alge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integrable System
In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first integrals, that its motion is confined to a submanifold of much smaller dimensionality than that of its phase space. Three features are often referred to as characterizing integrable systems: * the existence of a ''maximal'' set of conserved quantities (the usual defining property of complete integrability) * the existence of algebraic invariants, having a basis in algebraic geometry (a property known sometimes as algebraic integrability) * the explicit determination of solutions in an explicit functional form (not an intrinsic property, but something often referred to as solvability) Integrable systems may be seen as very different in qualitative character from more ''generic'' dynamical systems, which are more typically chaotic syste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
