# Skyrmion

﻿
Skyrmion

In theoretical physics, a skyrmion, conceived by Tony Skyrme, is a mathematical model used to model baryons (a subatomic particle).A skyrmion is a homotopically non-trivial classical solution of a nonlinear sigma model with a non-trivial target manifold topology: a particular case of a topological soliton. It arises, for example, in chiral models of mesons where the target manifold is a homogeneous space of

:$SU\left(N\right)_L imes SU\left(N\right)_R ,$

(the structure group),

:$left\left(frac\left\{SU\left(N\right)_L imes SU\left(N\right)_R\right\}\left\{SU\left(N\right)_\left\{diag ight\right)$

where

:SU(N)L and SU(N)R are the left and right copies respectively

:SU(N)diag is the diagonal subgroup

If spacetime has the topology S3&times;R (for space and time respectively), then classical configurations are classified by an integral winding number because the third homotopy group,

:$pi_3left\left(frac\left\{SU\left(N\right)_L imes SU\left(N\right)_R\right\}\left\{SU\left(N\right)_\left\{diagcong SU\left(N\right) ight\right)=mathbb\left\{Z\right\}$

(the congruence sign here refers to homeomorphism, not isomorphism).

It is possible to add a topological term to the chiral lagrangian whose integral only depends upon the homotopy class. This results in superselection sectors in the quantized model.

Skyrmions have been used to model baryons.

* [http://arxiv.org/abs/hep-ph/0202250 hep-ph/0202250 Stephen Wong: What exactly is a Skyrmion?]

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• skyrmion — /skûrˈmi on/ (physics) noun (in a non linear field theory) a soliton (qv) with spin and statistics different from those of the underlying fields ORIGIN: Tony Skyrme (1922–87), English physicist …   Useful english dictionary

• Skyrmion — Als Skyrmion (nach Tony Skyrme) wird in der theoretischen Physik ein Modell aus dem Bereich der Topologie für stabile Wirbel in Feldern bezeichnet. Diese Wirbel verhalten sich wie Teilchen bzw. Quasiteilchen endlicher Masse. Das Modell ist aus …   Deutsch Wikipedia

• skyrmion — noun A topological soliton used in the mathematical modelling of baryons …   Wiktionary

• Nucleon — For the Ford concept car, see Ford Nucleon. For the fictional power source in the Transformers universe, see Nucleon (Transformers). An atomic nucleus is a compact bundle of the two types of nucleons: Protons (red) and neutrons (blue). In this… …   Wikipedia

• Topological defect — Also see base concepts: topology, differential equations, quantum theory condensed matter physics .In mathematics and physics, a topological soliton or a topological defect is a solution of a system of partial differential equations or of a… …   Wikipedia

• List of particles — This is a list of the different types of particles, known and hypothesized. For a chronological listing of subatomic particles by discovery date, see Timeline of particle discoveries. This is a list of the different types of particles found or… …   Wikipedia

• Skyrme — Tony Hilton Roy Skyrme (* 5. Dezember 1922 in Lewisham, Kent; † 25. Juni 1987) war ein britischer theoretischer Physiker, der sich mit Kernphysik beschäftigte. Leben und Wirken Skyrme besuchte Eton College ab 1936 und ging 1940 mit einem… …   Deutsch Wikipedia

• Скирмион — Скирмион  математическая модель, применяемая для моделирования барионов. Автор Тони Скайрми. Содержание …   Википедия

• Electron — For other uses, see Electron (disambiguation). Electron Experiments with a Crookes tube first demonstrated the particle nature of electrons. In this illustration, the profile of the cross shaped target is projected against the tube face at right… …   Wikipedia

• Fermion — In particle physics, fermions are particles which obey Fermi Dirac statistics; they are named after Enrico Fermi. In contrast to bosons, which have Bose Einstein statistics, only one fermion can occupy a quantum state at a given time; this is the …   Wikipedia