Feynman Propagator for a Free Scalar Field on a Causal Set

TL;DR

This paper introduces a Lorentz invariant discretisation of spacetime using causal sets to define a Feynman propagator for a free scalar quantum field, providing a novel regularisation method.

Contribution

It develops a formalism for scalar quantum fields on causal sets, including operators and vacuum state, as a new approach to regularising quantum field theory.

Findings

Defines scalar field operators on causal sets

Constructs a vacuum state for the theory

Proposes a Lorentz invariant regularisation scheme

Abstract

The Feynman propagator for a free bosonic scalar field on the discrete spacetime of a causal set is presented. The formalism includes scalar field operators and a vacuum state which define a scalar quantum field theory on a causal set. This work can be viewed as a novel regularisation of quantum field theory based on a Lorentz invariant discretisation of spacetime.