The continuum limit of a 4-dimensional causal set scalar d'Alembertian. (1st December 2016) - Belenchia, Alessio; Benincasa, Dionigi M T; Dowker, Fay
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 □ . 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 □ − 1 2 R, where R is the Ricci scalar, under certain conditions on the spacetime and the scalar field.