Quantum Field Theory on Causal Sets

We give a broad overview of a construction of a theory for matter on fixed causal set backgrounds. We introduce the Sorkin-Johnston formalism for a free (real) scalar field theory that is applicable to regions of continuum spacetimes as well as to causal sets. We show examples in the causal set, starting from the construction of Green functions to obtaining unique two-point functions using this formalism. We also mention other approaches that have been explored in constructing dynamics for matter on causal sets, including ideas for interacting theories and fermions.