where SU(N)L and SU(N)R are the left and right copies respectively and 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, (the congruence sign here refers to homeomorphism, not isomorphism).
It's 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.
External links
hep-ph/0202250 Stephen Wong: What exactly is a Skyrmion? (http://arxiv.org/abs/hep-ph/0202250)
In this limit, the shape of the spin distribution within the core of Skyrmion is not affected, neither by the Zeeman splitting nor by the Coulomb energy, and is the same as that of an ideal Skyrmion.
In the paper [6] another approach to the problem of Skyrmions is offered by using transformation induced by application of a non-reduced to the same Landau level states rotation matrix and considering the full Schrodinger equation obtained by means of ordinary perturbation theory applied to the gradients of this matrix.
The propagation of spin waves in the presence of a single Skyrmion in the framework of the proposed approach was considered.
The skyrmions are not point particles, so it is not immediately obvious how to construct a Hamiltonian, or a Schrodinger equation for them.
The `skyrmions' are twists in the magnetisation of the system, and their influence on the - linear - spin waves will be investigated.
Then a variational approach to the quantum case will be considered, where approximate momentum eigenstates of the skyrmions will be constructed and their energy as a function of wave vector investigated.
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