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

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Title: The continuum limit of a 4-dimensional causal set scalar d’Alembertian
Authors: Belenchia, A
Benincasa, DMT
Dowker, F
Item Type: Journal Article
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.
Issue Date: 1-Dec-2016
Date of Acceptance: 28-Oct-2016
ISSN: 0264-9381
Publisher: IOP Publishing
Journal / Book Title: Classical and Quantum Gravity
Volume: 33
Copyright Statement: © 2016 IOP Publishing Ltd. 'This is an author-created, un-copyedited version of an article accepted for publication in Classical and Quantum Gravity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher authenticated version is available online at
Sponsor/Funder: Science and Technology Facilities Council (STFC)
Funder's Grant Number: ST/L00044X/1
Keywords: gr-qc
Nuclear & Particles Physics
02 Physical Sciences
01 Mathematical Sciences
Notes: journal_title: Classical and Quantum Gravity article_type: paper article_title: The continuum limit of a 4-dimensional causal set scalar d’Alembertian copyright_information: © 2016 IOP Publishing Ltd date_received: 2016-05-16 date_accepted: 2016-10-28 date_epub: 2016-12-01
Publication Status: Published
Article Number: 245018
Appears in Collections:Physics
Theoretical Physics
Faculty of Natural Sciences

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