Search results
Results From The WOW.Com Content Network
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 ...
In physics, a sigma model is a field theory that describes the field as a point particle confined to move on a fixed manifold. This manifold can be taken to be any Riemannian manifold, although it is most commonly taken to be either a Lie group or a symmetric space.
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.
Still, nonlinear sigma models transform nonlinearly, so there are applications. If there is a principal bundle P whose base space is space or spacetime and structure group is a Lie group, then the sections of P form a principal homogeneous space of the group of gauge transformations.
The idea is related to a property of the bosonic string in a curve background, better known as nonlinear sigma model. First calculations from this model [2] showed as the beta function, representing the running of the metric of the model as a function of an energy scale, is proportional to the Ricci tensor giving rise to a Ricci flow.
The second-largest U.S. producer is partnering with investment firm Engine No. 1 and electric services company GE Vernova on the project. Chevron's announcement comes a day after Chinese startup ...
The model is a system of three ordinary differential equations now known as the Lorenz equations: ... sigma, rho, beta]: ... Chaos and Nonlinear Dynamics: ...