2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/204021A quantum mechanical description of particle propagation on the discrete spacetime of a causal set is presented. The model involves a discrete path integral in which trajectories within the causal set are summed over to obtain a particle propagator. The sum-over-trajectories is achieved by a matrix geometric series. For causal sets generated by sprinkling points into 1+1 and 3+1 dimensional Minkowski spacetime the propagator calculated on the causal set is shown to agree, in a suitable sense, with the causal retarded propagator for the Klein-Gordon equation. The particle propagator described here is a step towards quantum field theory on causal set spacetime.14 pages, no figures. Minor updates to match published versionHigh Energy Physics - TheoryGeneral Relativity and Quantum Cosmologytext