Consistent Laplacian on Geodesic Causal Sets

Details Consistent Laplacian on Geodesic Causal Sets Consistent Laplacian on Geodesic Causal Sets

Mar 2012

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012aps..apr.l8006b&link_type=abstract

American Physical Society, APS April Meeting 2012, March 31-Apr 3, 2012, abstract #L8.006

Physics

Scientific paper

Causal sets are directed simple graphs with partial ordering. They describe spacetime at the smallest scales, and are thought to be a suitable starting point for a theory of quantum gravity. Laplacians and related linear operators on discrete sets form the basis for derivative operators in the continuum limit. We explore the relation between Laplacian operators and the structures of geodesic causal sets, non-geodesic causal sets, and directed graphs with causal loops. Laplacian spectra are calculated and used to define effective distances (invariant intervals) between points on causal sets.

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