Scalar Field Theory on a Causal Set in Histories form

Abstract

We recast into histories-based form a quantum field theory defined earlier in operator language for a free scalar field on a background causal set. The resulting decoherence functional resembles that of the continuum theory but the counterpart of the d'Alembertian operator is nonlocal and a generalized inverse of the discrete retarded Green function. We comment on the significance of this and we also suggest how to include interactions. © Published under licence by IOP Publishing Ltd.