# Skyrmion

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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?]

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