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(N)_L imes SU(N)_R ,

(the structure group),

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

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×R (for space and time respectively), then classical configurations are classified by an integral winding number because the third homotopy group,

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

(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.

External links

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


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