  Field theories on the Groenewold-Moyal(GM) plane are studied using the
Lehmann-Symanzik-Zimmermann(LSZ) formalism. The example of real scalar fields
is treated in detail. The S-matrix elements in this non-perturbative approach
are shown to be equal to the interaction representation S-matrix elements. This
is a new non-trivial result: in both cases, the S-operator is independent of
the noncommutative deformation parameter $\theta_{\mu\nu}$ and the change in
scattering amplitudes due to noncommutativity is just a time delay. This result
is verified in two different ways. But the off-shell Green's functions do
depend on $\theta_{\mu\nu}$. In the course of this analysis, unitarity of the
non-perturbative S-matrix is proved as well.
