- Skyrmion
In
theoretical physics , a skyrmion, conceived byTony Skyrme , is a mathematical model used to modelbaryon s (asubatomic particle ).A skyrmion is a homotopically non-trivial classical solution of anonlinear sigma model with a non-trivialtarget manifold topology : a particular case of atopological soliton . It arises, for example, inchiral model s of mesons where the target manifold is ahomogeneous 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 thirdhomotopy 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 sector s in the quantized model.Skyrmions have been used to model
baryon s.External links
* [http://arxiv.org/abs/hep-ph/0202250 hep-ph/0202250 Stephen Wong: What exactly is a Skyrmion?]
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