The causal set reduction formula

Abstract

We derive a reduction formula for matrix elements on a causal set background. We derive an infinite tower of relations between correlators, akin to the Schwinger-Dyson equations of the continuum. Combining these two results we are able to express matrix elements in three different forms: as a path integral and as two distinct sums of correlators. We sketch the form that our method - which circumvents explicit use of differential equation of motion operators - takes in flat continuum spacetime where it provides an alternative expression for the standard LSZ result.