Correction terms for propagators and d’Alembertians due to spacetime discreteness

Abstract

The causal set approach to quantum gravity models spacetime as a discrete structure—a causal set. Recent research has led to causal set models for the retarded propagator for the Klein–Gordon equation and the d’Alembertian operator. These models can be compared to their continuum counterparts via a sprinkling process. It has been shown that the models agree exactly with the continuum quantities in the limit of an infinite sprinkling density—the continuum limit. This paper obtains the correction terms for these models for sprinkled causal sets with a finite sprinkling density. These correction terms are an important step towards testable differences between the continuum and discrete models that could provide evidence of spacetime discreteness.