Consistent construction of perturbation theory on non-commutative spaces

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 on a non-commutative 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 non-commutativity 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.