The directional charges are different for an electron that has always been at rest and an electron that has always been moving at a certain nonzero velocity (because of the Lorentz transformations). The conclusion is that both electrons lie in different superselection sectors no matter how tiny the velocity is. At first sight, this might appear to be in contradiction with Wigner's classification, which implies that the whole one-particle Hilbert space lies in a single superselection sector, but it is not because "m" is really the greatest lower bound of a continuous mass spectrum and eigenstates of "m" only exist in a rigged Hilbert space. The electron, and other particles like it is called an infraparticle.