  We study quantum electrodynamics on the noncommutative Minkowski space in the
Yang-Feldman formalism. Local observables are defined by using covariant
coordinates. We compute the two-point function of the interacting field
strength to second order and find the infrared divergent terms already known
from computations using the so-called modified Feynman rules. It is shown that
these lead to nonlocal renormalization ambiguities. Also new nonlocal
divergences stemming from the covariant coordinates are found. Furthermore, we
study the supersymmetric extension of the model. For this, the supersymmetric
generalization of the covariant coordinates is introduced. We find that the
nonlocal divergences cancel. At the one-loop level, the only effect of
noncommutativity is then a momentum-depenent field strength normalization. We
interpret it as an acausal effect and show that its range is independent of the
noncommutativity scale.
