Scalar Field Theory on a Causal Set in Histories Form

TL;DR

This paper reformulates a free scalar quantum field theory on a causal set into a histories-based framework, highlighting the nonlocal d'Alembertian operator and discussing potential for including interactions.

Contribution

It introduces a histories-based formulation of scalar field theory on causal sets, providing a new perspective and tools for quantum gravity research.

Findings

Decoherence functional resembles continuum theory

Nonlocal d'Alembertian as inverse of Green function

Framework suggests ways to incorporate interactions

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. The counterpart of the d'Alembertian operator is nonlocal and is a generalized inverse of the discrete retarded Green function. We comment on the significance of this and we also suggest how to include interactions.