Scalar Curvature of a Causal Set

Dionigi M. T. Benincasa and Fay Dowker
Phys. Rev. Lett. 104, 181301 – Published 6 May 2010

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 parametrized by the scale of the nonlocality, and approximate the continuum scalar D’Alembertian 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 12R where R is the Ricci scalar curvature. This can used to define an approximately local action functional for causal sets.

  • Received 15 January 2010

DOI:https://doi.org/10.1103/PhysRevLett.104.181301

©2010 American Physical Society

Authors & Affiliations

Dionigi M. T. Benincasa and Fay Dowker

  • Blackett Laboratory, Imperial College, London SW7 2AZ, United Kingdom

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Issue

Vol. 104, Iss. 18 — 7 May 2010

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