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 languageEnglish
JournalClassical and Quantum Gravity
DOIs
Publication statusPublished - 01 Dec 2016
Externally publishedYes

Keywords

  • causal set
  • wave equation
  • non locality

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