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 J-vector = L-vector+S-vector. 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.