The Scalar Curvature of a Causal Set

Abstract

A one parameter family of retarded linear operators on scalar fields on causal sets is introduced. When the causal set is well-approximated by 4 dimensional Minkowski spacetime, the operators are Lorentz invariant but nonlocal, are parametrised by the scale of the nonlocality and approximate the continuum scalar D'Alembertian, $\square$, when acting on fields that vary slowly on the nonlocality scale. The same operators can be applied to scalar fields on causal sets which are well-approximated by curved spacetimes in which case they approximate $\square -1/2R$ where $R$ is the Ricci scalar curvature. This can used to define an approximately local action functional for causal sets.

Typo in definition of equation (3) and definition of n(x,y) corrected. Note: published version still contains typo

References in corpus (1)

• The Nonperturbative Quantum de Sitter Universe

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