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

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.

31 pages, 2 figures. Slightly revised version, accepted for publication in Classical and Quantum Gravity

References in corpus (5)

• Generalized Causal Set d'Alembertians
• Fermi Coordinates and Penrose Limits
• Nonlocal Scalar Quantum Field Theory from Causal Sets
• Low energy signatures of nonlocal field theories
• Dark Matter From Spacetime Nonlocality

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