  We examine the effect of non-local deformations on the applicability of
interaction point time ordered perturbation theory (IPTOPT) based on the free
Hamiltonian of local theories. The usual argument for the case of quantum field
theory (QFT) on a noncommutative (NC) space (based on the fact that the
introduction of star products in bilinear terms does not alter the action) is
not applicable to IPTOPT due to several discrepancies compared to the naive
path integral approach when noncommutativity involves time. These discrepancies
are explained in detail. Besides scalar models, gauge fields are also studied.
For both cases, we discuss the free Hamiltonian with respect to non-local
deformations.
