Scalar Field Theory on a Causal Set in Histories Form

Understand

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.