The continuum limit of a 4-dimensional causal set scalar d’Alembertian
File(s)
Accepted version
Author(s)
Belenchia, A
Benincasa, DMT
Dowker, F
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.
Date Issued
2016-12-01
Date Acceptance
2016-10-28
Citation
Classical and Quantum Gravity, 2016, 33
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
Science and Technology Facilities Council (STFC)
Grant Number
ST/L00044X/1
Subjects
gr-qc
hep-th
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