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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 mathematical optimization, the problem of non-negative least squares (NNLS) is a type of constrained least squares problem where the coefficients are not allowed to become negative.
The unscented Kalman filter (UKF) [67] uses a deterministic sampling technique known as the unscented transformation (UT) to pick a minimal set of sample points (called sigma points) around the mean. The sigma points are then propagated through the nonlinear functions, from which a new mean and covariance estimate are then formed.
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
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.
The Voigt profile is normalized: (;,) =,since it is a convolution of normalized profiles. The Lorentzian profile has no moments (other than the zeroth), and so the moment-generating function for the Cauchy distribution is not defined.
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