Path Sums for Propagators in Causal Sets

A major challenge in Causal Set research is that theories need only to match general relativity and quantum field theory in the appropriate limits. This means that there should be many different ways to calculate a scalar field propagator in a causal set that match the known limits, but may give significantly different results on the small scale. In this work, we explore under what conditions a path sum will correspond to a scalar field propagator in such a way that it matches the known value in the continuum limit. A family of solutions for the path sum is found and is verified numerically in a few specific cases.