# The continuum limit of a 4-dimensional causal set scalar d'Alembertian

A. Belenchia, D.M.T. Benincasa*, F. Dowker

*Corresponding author for this work

Research output: Contribution to journalArticle

6 Citations (Scopus)

### Abstract

The continuum limit of a 4-dimensional, discrete d'Alembertian operator for scalar fields on causal sets is studied. The continuum limit of the mean of this operator in the Poisson point process in 4-dimensional Minkowski spacetime is shown to be the usual continuum scalar d'Alembertian $\square$ . It is shown that the mean is close to the limit when there exists a frame in which the scalar field is slowly varying on a scale set by the density of the Poisson process. The continuum limit of the mean of the causal set d'Alembertian in 4-dimensional curved spacetime is shown to equal $\square -\frac{1}{2}R$ , where R is the Ricci scalar, under certain conditions on the spacetime and the scalar field.
Original language English Classical and Quantum Gravity https://doi.org/10.1088/0264-9381/33/24/245018 Published - 01 Dec 2016 Yes

### Keywords

• causal set
• wave equation
• non locality