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

File Description SizeFormat
1510.04656v2.pdfFile embargoed until 01 December 2017675.16 kBAdobe PDF
 Title: The continuum limit of a 4-dimensional causal set scalar d’Alembertian Author(s): Belenchia, ABenincasa, DMTDowker, 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. Publication Date: 1-Dec-2016 Date of Acceptance: 28-Oct-2016 URI: http://hdl.handle.net/10044/1/43575 DOI: http://dx.doi.org/10.1088/0264-9381/33/24/245018 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 http://dx.doi.org/10.1088/0264-9381/33/24/245018 Sponsor/Funder: Science and Technology Facilities Council (STFC) Funder's Grant Number: ST/L00044X/1 Keywords: gr-qcgr-qchep-thNuclear & Particles Physics02 Physical Sciences01 Mathematical Sciences Publication Status: Published Article Number: 245018 Embargo Date: 2017-12-01 Appears in Collections: PhysicsTheoretical PhysicsFaculty of Natural Sciences