Causal set d'Alembertians for various dimensions

TL;DR

This paper introduces a Lorentz invariant discrete operator for scalar fields in various dimensions, approximating the Minkowski d'Alembertian, and proposes a causal set action based on scalar curvature estimation.

Contribution

It presents a new discrete Lorentz invariant operator for scalar fields in different dimensions and develops a causal set action using scalar curvature estimation.

Findings

Provides a Lorentz invariant operator approximating the d'Alembertian

Establishes a scalar curvature estimator for causal sets

Proposes a causal set action based on curvature

Abstract

We propose, for dimension d, a discrete Lorentz invariant operator on scalar fields that approximates the Minkowski spacetime scalar d'Alembertian. For each dimension, this gives rise to a scalar curvature estimator for causal sets, and thence to a proposal for a causal set action.