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arXiv · 1510.04656

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

Alessio Belenchia·Dionigi M. T. Benincasa·Fay Dowker
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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 $\Box$. 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 $\Box - \frac{1}{2}R$, where $R$ is the Ricci scalar, under certain conditions on the spacetime and the scalar field.

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Alessio Belenchia, Dionigi M. T. Benincasa, Fay Dowker. 2016-10-30. The continuum limit of a 4-dimensional causal set scalar d'Alembertian. https://doi.org/10.1088/0264-9381%2F33%2F24%2F245018

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