Particles in non-Abelian gauge potentials: Landau problem and insertion of non-Abelian flux

In this paper, we study charged spin-1/2 particles in two dimensions, subjected
to a perpendicular non-Abelian magnetic field. Specializing to a choice of vector potential that is
spatially constant but non-Abelian, we investigate the Landau level spectrum in planar and spherical
geometry, paying particular attention to the role of the total angular momentum J⃗ = L⃗ + S⃗. Then,
we show that the adiabatic insertion of non-Abelian flux in a spin-polarized quantum Hall state
leads to the formation of charged spin textures, which in the simplest cases can be identified with
quantum Hall Skyrmions.