A closed form expression for the causal set d'Alembertian

Abstract

Recently a definition for a Lorentz invariant operator approximating the d'Alembertian in d-dimensional causal set space-times has been proposed. This operator contains several dimension-dependent constants which have been determined for d=2,...,7. In this note we derive closed form expressions for these constants, which are valid in all dimensions. Using these we prove that the causal set action in any dimension can be defined through this discrete d'Alembertian, with a dimension independent prefactor.