We consider an electron which is electromagnetically dressed in such a
way that it is both gauge invariant and that it has the associated el
ectric and magnetic fields expected of a moving charge, We study the p
ropagator of this dressed electron and, for small velocities, show exp
licitly at one loop that at the natural (on-shell) renormalisation poi
nt, p(0) = m,p = mv, one can renormalise the propagator multiplicative
ly. Furthermore the renormalisation constants are infra-red finite. Th
is shows that the dressing we use corresponds to a slowly moving, phys
ical asymptotic field.