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Time ordered perturbation theory for non-local interactions; applications to NCQFT

In the past decades, time ordered perturbation theory was very successful in describing relativistic scattering processes. It was developed for local quantum field theories. However, there are field theories which are governed by non-local interactions, for example non-commutative quantum field theory (NCQFT). Filk (Phys. Lett. B 376 (1996) 53) first studied NCQFT perturbatively obtaining the usual Feynman propagator and additional phase factors as the basic elements of perturbation theory. However, this treatment is only applicable for cases, where the deformation of space-time does not involve time. Thus, we generalize Filk's approach in two ways: First, we study non-local interactions of a very general type able to embed NCQFT. And second, we also include the case, where non-locality involves time. A few applications of the obtained formalism will also be discussed.