Skyrmions are a class of solitons, which are both topologically stable, meaning that their vacuum manifold has a non-trivial π_3 homotopy group, and energetically stable, meaning that they are local minima of the field energy. The non-linear sigma model is an effective hadronic field theory, based on a triplet of pion fields, which is a low energy approximation to QCD. With the addition of the Skyrme term, this approximate model may be improved to yield skyrmion solutions. Further improvements to the model allow us to give the pion fields mass. By considering a 'spherically symmetric', energy-minimising skyrmion solution corresponding to a winding number of B=1, we deduce that the skyrmion has a mass of ~1 GeV and a RMS radius of ~1 fm. By imposing CPT symmetry on the theory, we require the addition of the Wess-Zumino term to the action. From a calculation of the Noether charge corresponding to the baryon number symmetry group, U(1)_V, we deduce that the baryon number corresponds to the winding number of the skyrmion, which suggests that skyrmions are the baryons of QCD. By canonically quantizing the rotation of the B=1 skyrmion and imposing electromagnetic gauge, we deduce the spin, isospin and physical electric charge. This supports the hypothesis that skyrmions correspond to baryons, and we identify the skyrmions corresponding to the proton and the neutron. Extending the theory, we discuss how light nuclei, with B<7, may be successfully modeled using the single rational map ansatz. We briefly review the complications that arise when modeling larger nuclei (B≥7) and show that certain higher-order skyrmions may be successfully constructed using geometric rational map ansätze based on the Skyrme crystal.
2015-04-30Part III Essay