  Assuming the S-matrix on noncommutative (NC) spacetime can still be
developped perturbatively in terms of the time-ordered exponential of the
interaction Lagrangian, we investigate the perturbation theory of NC field
theory. We first work out with care some typical Green functions starting from
the usual concepts of time-ordering and commutation relations for free fields.
The results are found to be very different from those in the naive approach
pursued in the literature. A simple framework then appears naturally which can
incorporate the new features of our results and which turns out to be the usual
time-ordered perturbation theory extended to the NC context. We provide the
prescriptions for computing S-matrix elements and Green functions in this
framework. We also emphasize that the naive seemingly covariant approach cannot
be reproduced from the current one, in contrast to the field theory on ordinary
spacetime. We attribute this to the phase-like nonlocal interaction intrinsic
in NC field theory which modifies the analytic properties of Green functions
significantly.
