Causal set actions in various dimensions

Causal set theory is a discrete approach to quantum gravity. The idea is that space-time is not a smooth manifold but a discrete causal set. This means that differential structure can not be assumed but has to be replaced by discrete alternatives. In this paper a pattern for a discrete version of the scalar D'Alembertian operator in various dimensions is proposed and tested. Corrections to this operator in curved space-time are proportional to the curvature scalar, and the proportionality constant is calculated for various dimensions. These corrections can be used to define a Causal Set action which is then calculated for various dimensions.