  The non-commutative Wess-Zumino model is used as a prototype for studying the
low energy behaviour of a renormalizable non-commutative field theory. We start
by deriving the potential mediating the fermion-fermion and boson-boson
interactions in the non-relativistic regime. The quantum counterparts of these
potentials are afflicted by irdering ambiguities but we show that there exists
an ordering prescription which makes them hermitean. For space/space
noncommutativity it turns out that Majorana fermions may be pictured as rods
oriented perpendicularly to the direction of motion showing a lack of
localituy, while bosons remain insensitive to the effects of noncommutativity.
For time/space noncommutativity bosopns and fermions can be regarded as rods
oriented along the direction of motion. For both cases of noncommutativity the
scattering state described scattered waves, with at least one wave having
negative time delay signalizing the underlying nonlocality. The superfield
formulation of the model is used to compute the corresponding effective action
in the one- and two-loop approximations. In the case of time/space
noncommutativity, unitarity is violated in the relativistic regime. However,
this does not preclude the existence of the unitary low energy limit.
