### 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 |
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Journal | Classical and Quantum Gravity |

DOIs | |

Publication status | Published - 01 Dec 2016 |

Externally published | Yes |

### Keywords

- causal set
- wave equation
- non locality

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## Cite this

Belenchia, A., Benincasa, D. M. T., & Dowker, F. (2016). The continuum limit of a 4-dimensional causal set scalar d'Alembertian.

*Classical and Quantum Gravity*. https://doi.org/10.1088/0264-9381/33/24/245018