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Bullough–Dodd Model
The Bullough–Dodd model is an integrable model in 1+1-dimensional quantum field theory introduced by Robin Bullough and Roger Dodd. Its Lagrangian density is :\mathcal=\frac(\partial_\mu\varphi)^2-\frac(2e^ +e^) where m_0\, is a mass parameter, g\, is the coupling constant and \varphi\, is a real scalar field. The Bullough–Dodd model belongs to the class of affine Toda field theories. The spectrum of the model consists of a single massive particle. See also *List of integrable models This is a list of integrable models as well as classes of integrable models in physics. Integrable models in 1+1 dimensions In classical and quantum field theory: *free boson *free fermion * sine-Gordon model * Thirring model * sinh-Gordon mo ... References * * Quantum field theory Exactly solvable models Integrable systems {{quantum-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integrable Model
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] |
Robin Bullough
Robin K. Bullough (21 November 1929 – 30 August 2008) was a British mathematical physicist known for his contributions to the theory of solitons, in particular for his role in the development of the theory of the optical soliton, now commonly used, for example, in the theory of trans-oceanic optical fibre communication theory, but first recognised in Bullough's work on ultra-short (nano- and femto-second) optical pulses. He is also known for deriving exact solutions to the nonlinear equations describing these solitons and for associated work on integrable systems, infinite-dimensional Hamiltonian systems (both classical and quantum), and the statistical mechanics for these systems. Bullough also contributed to nonlinear mathematical physics, including Bose–Einstein condensation in magnetic traps. Bullough obtained his first academic position in the Mathematics Department at UMIST in 1960 and was appointed chair of Mathematical Physics in 1973 where he remained until his ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roger Dodd
Roger is a masculine given name, and a surname. The given name is derived from the Old French personal names ' and '. These names are of Germanic languages">Germanic origin, derived from the elements ', ''χrōþi'' ("fame", "renown", "honour") and ', ' ("spear", "lance") (Hrōþigēraz). The name was introduced into England by the Normans. In Normandy, the Franks, Frankish name had been reinforced by the Old Norse cognate '. The name introduced into England replaced the Old English cognate '. ''Roger'' became a very common given name during the Middle Ages. A variant form of the given name ''Roger'' that is closer to the name's origin is '' Rodger''. Slang and other uses From up to , Roger was slang for the word "penis". In ''Under Milk Wood'', Dylan Thomas writes "jolly, rodgered" suggesting both the sexual double entendre and the pirate term "Jolly Roger". In 19th-century England, Roger was slang for another term, the cloud of toxic green gas that swept through the chlori ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lagrangian Density
Lagrangian field theory is a formalism in classical field theory. It is the field-theoretic analogue of Lagrangian mechanics. Lagrangian mechanics is used to analyze the motion of a system of discrete particles each with a finite number of degrees of freedom. Lagrangian field theory applies to continua and fields, which have an infinite number of degrees of freedom. One motivation for the development of the Lagrangian formalism on fields, and more generally, for classical field theory, is to provide a clear mathematical foundation for quantum field theory, which is infamously beset by formal difficulties that make it unacceptable as a mathematical theory. The Lagrangians presented here are identical to their quantum equivalents, but, in treating the fields as classical fields, instead of being quantized, one can provide definitions and obtain solutions with properties compatible with the conventional formal approach to the mathematics of partial differential equations. This enabl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coupling Constant
In physics, a coupling constant or gauge coupling parameter (or, more simply, a coupling), is a number that determines the strength of the force exerted in an interaction. Originally, the coupling constant related the force acting between two static bodies to the " charges" of the bodies (i.e. the electric charge for electrostatic and the mass for Newtonian gravity) divided by the distance squared, r^2, between the bodies; thus: G in F=G m_1 m_2/r^2 for Newtonian gravity and k_\text in F=k_\textq_1 q_2/r^2 for electrostatic. This description remains valid in modern physics for linear theories with static bodies and massless force carriers. A modern and more general definition uses the Lagrangian \mathcal (or equivalently the Hamiltonian \mathcal) of a system. Usually, \mathcal (or \mathcal) of a system describing an interaction can be separated into a ''kinetic part'' T and an ''interaction part'' V: \mathcal=T-V (or \mathcal=T+V). In field theory, V always contains 3 fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Toda Field Theory
In mathematics and physics, specifically the study of field theory and partial differential equations, a Toda field theory, named after Morikazu Toda, is specified by a choice of Lie algebra and a specific Lagrangian. Formulation Fixing the Lie algebra to have rank r, that is, the Cartan subalgebra of the algebra has dimension r, the Lagrangian can be written \mathcal=\frac\left\langle \partial_\mu \phi, \partial^\mu \phi \right\rangle -\frac\sum_^r n_i \exp(\beta \langle\alpha_i, \phi\rangle). The background spacetime is 2-dimensional Minkowski space, with space-like coordinate x and timelike coordinate t. Greek indices indicate spacetime coordinates. For some choice of root basis, \alpha_i is the ith simple root. This provides a basis for the Cartan subalgebra, allowing it to be identified with \mathbb^r. Then the field content is a collection of r scalar fields \phi_i, which are scalar in the sense that they transform trivially under Lorentz transformations of the underly ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Integrable Models
This is a list of integrable models as well as classes of integrable models in physics. Integrable models in 1+1 dimensions In classical and quantum field theory: *free boson *free fermion * sine-Gordon model * Thirring model * sinh-Gordon model *Liouville field theory * Bullough–Dodd model *Dym equation *Calogero–Degasperis–Fokas equation *Camassa–Holm equation * Drinfeld–Sokolov–Wilson equation * Benjamin–Ono equation *SS model *sausage model * Toda field theories *O(''N'')-symmetric non-linear sigma models *Ernst equation * massless Schwinger model *supersymmetric sine-Gordon model *supersymmetric sinh-Gordon model * conformal minimal models *critical Ising model *tricritical Ising model *3-state Potts model *various perturbations of conformal minimal models *superconformal minimal models *Wess–Zumino–Witten model * Nonlinear Schroedinger equation * Korteweg–de Vries equation * modified Korteweg–de Vries equation *Gardner equation * Gibbons–Tsarev equ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Field Theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. The current standard model of particle physics is based on QFT. History Quantum field theory emerged from the work of generations of theoretical physicists spanning much of the 20th century. Its development began in the 1920s with the description of interactions between light and electrons, culminating in the first quantum field theory—quantum electrodynamics. A major theoretical obstacle soon followed with the appearance and persistence of various infinities in perturbative calculations, a problem only resolved in the 1950s with the invention of the renormalization procedure. A second major barrier came with QFT's apparent inabili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exactly Solvable Models
Exact may refer to: * Exaction, a concept in real property law * ''Ex'Act'', 2016 studio album by Exo * Schooner Exact, the ship which carried the founders of Seattle Companies * Exact (company), a Dutch software company * Exact Change, an American independent book publishing company * Exact Editions, a content management platform Mathematics * Exact differentials, in multivariate calculus * Exact algorithms, in computer science and operations research * Exact colorings, in graph theory * Exact couples, a general source of spectral sequences * Exact sequences, in homological algebra * Exact functor, a function which preserves exact sequences See also * *Exactor (other) *XACT (other) *EXACTO, a sniper rifle {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
