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In this paper we address the non-locality issue of quantum field theory on acausal set by rewriting it in such a way that avoids the use of d'Alembertian.We do that by replacing scalar field over points with scalar field over edges,where the edges are taken to be very long rather than very short. Inparticular, they are much longer than the size of the laboratory. Due to theirlarge length, we can single out the edges that are almost parallel to eachother, and then use directional derivatives in the direction of those edges (asopposed to d'Alembertian) along with a constraint that the derivatives aresmall in the direction perpendicular to those edges, in order to come up with aplane wave. The scalar field is thought to reside at the future end of thoseedges, which renders the seemingly nonlocal effects of their large length asphysically irrelevant. After that we add by hand the interaction of those planewaves that would amount to 4-vertex coupling of plane waves.

Restoring locality of scalar fields on a causal set by avoiding the use of d'Alembertians