Path integrals on causal sets

We describe a quantum mechanical model for particle propagation on a causal set. The model involves calculating a particle propagator by summing amplitudes assigned to trajectories within the causal set. This "discrete path integral" is calculated using a matrix geometric series. Amplitudes are given which, when the causal set is generated by sprinkling points into 1+1 or 3+1 Minkowski spacetime, ensure the particle propagator agrees in a suitable sense, with the retarded causal propagator for the Klein-Gordon equation.