2010/01/31 by Dionigi M. T. Benincasa, Fay Dowker · 2 citations
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevlett.104.181301
published as Phys.Rev.Lett.104:181301,2010 · Typo in definition of equation (3) and definition of n(x,y) corrected. Note: published version still contains typo
openalex publication_date 2010/05/06 · arxiv created 2011/11/01 · arxiv updated 2011/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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-(1/2)R where R is the Ricci scalar curvature. This can used to define an approximately local action functional for causal sets.