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

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 □....

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Bibliographic Details
Published in:Classical and quantum gravity 2016-12, Vol.33 (24), p.245018
Main Authors: Belenchia, Alessio, Benincasa, Dionigi M T, Dowker, Fay
Format: Article
Language:English
Subjects:
causal sets
curved spacetimes
non-locality
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Summary: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 □. 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 □−12R, where R is the Ricci scalar, under certain conditions on the spacetime and the scalar field.
ISSN:0264-9381
1361-6382
DOI:10.1088/0264-9381/33/24/245018