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

TL;DR

This paper extends time ordered perturbation theory to non-local quantum field theories, including those with time-involving non-locality, enabling better analysis of non-commutative quantum field theories.

Contribution

It generalizes Filk's approach to non-local interactions, incorporating cases where non-locality involves time, thus broadening the applicability of perturbation theory.

Findings

Developed a formalism for non-local interactions involving time.

Applied the formalism to specific non-commutative quantum field theories.

Enhanced understanding of perturbative methods for non-local QFTs.

Abstract

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.