Geometrical Aspects of Skyrmions, Reflection Group, and the Internal Symmetry of Hadrons

Abstract

The topological aspects of skyrmions are studied and it is shown that hadronscan be viewed as composite states of baby skyrmions when the internal symmetrySU(3) is generated from reflection. It is shown that in an anisotropic space aparticle can move with l = 1/2 with a specific lx value, and a bosonic constituentmoving with l = 1/2 will appear as a baby skyrmion and a fermionic constituentwill appear as if a spin carrier is attached to a baby skyrmion. The associatedmagnetic field causes a strong statistical attraction which helps to form the boundstate of such constituents. The doublet of such particles having opposite lx valuesform a conformal spinor when each member behaves as a Cartan semispinor.The conformal reflection then helps us to generate the internal SU(3) symmetry,which splits as SU(3) → SU(2) × U(1), giving rise to the hadronic spectra. Thestrong interaction involves a composite cluster in such a bound system whenrearrangement of the constituents takes place preserving the direction vectors,and an elementary constituent can take part in a weak interaction, causing parityviolation. These features help us to consider elementary constituents as knownparticles like leptons.