  We show that the classic results of Schwinger on the exact propagation of
particles in the background of constant field-strengths and plane waves can be
readily extended to the case of non-commutative QED. It is shown that
non-perturbative effects on constant backgrounds are the same as their
commutative counterparts, provided the on-shell gauge invariant dynamics is
referred to a non-perturbatively related space-time frame. For the case of the
plane wave background, we find evidence of the effective extended nature of
non-commutative particles, producing retarded and advanced effects in
scattering. Besides the known `dipolar' character of non-commutative neutral
particles, we find that charged particles are also effectively extended, but
they behave instead as `half-dipoles'.
