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The non-linear σ-model was introduced by Gell-Mann & Lévy (1960, §6), who named it after a field corresponding to a spinless meson called σ in their model. [1] This article deals primarily with the quantization of the non-linear sigma model; please refer to the base article on the sigma model for general definitions and classical (non ...
Unfortunately, the "sigma meson" is not described by the sigma-model, but only a component of it. [1] The sigma model was introduced by Gell-Mann & Lévy (1960, section 5); the name σ-model comes from a field in their model corresponding to a spinless meson called σ, a scalar meson introduced earlier by Julian Schwinger. [2]
In field theory, skyrmions are homotopically non-trivial classical solutions of a nonlinear sigma model [17] with a non-trivial target manifold topology – hence, they are topological solitons. An example occurs in chiral models [ 18 ] of mesons , where the target manifold is a homogeneous space of the structure group
NLopt (C/C++ implementation, with numerous interfaces including Julia, Python, R, MATLAB/Octave), includes various nonlinear programming solvers; SciPy (de facto standard for scientific Python) has scipy.optimize solver, which includes several nonlinear programming algorithms (zero-order, first order and second order ones).
Pages for logged out editors learn more. Contributions; Talk; Nonlinear sigma models
The four real quantities (π, σ) define the smallest nontrivial chiral multiplet and represent the field content of the linear sigma model. To switch from the above linear realization of SO(4) to the nonlinear one, we observe that, in fact, only three of the four components of ( π , σ ) are independent with respect to four-dimensional rotations.
It is a direct search method (based on function comparison) and is often applied to nonlinear optimization problems for which derivatives may not be known. However, the Nelder–Mead technique is a heuristic search method that can converge to non-stationary points [ 1 ] on problems that can be solved by alternative methods.
Non-linear sigma model is found in quantum field theory. Nonlinear system , in mathematics, represents a system whose behavior is not expressible as a linear function of its descriptors. A nonlinear X-wave (NLX) is a multi-dimensional wave that can travel without distortion.