On recovering continuum topology from a causal set
Type of Work
Article
Date
2007
Journal Title
Journal of Mathematical Physics
Journal ISSN
0022-2488
Journal Volume
48
Journal Issue
3
DOI
10.1063/1.2435599
Abstract
An important question that discrete approaches to quantum gravity must address is how continuum features of space-time can be recovered from the discrete substructure. Here, we examine this question within the causal set approach to quantum gravity, where the substructure replacing the space-timecontinuum is a locally finite partial order. A new topology on causal sets using “thickened antichains” is constructed. This topology is then used to recover the homology of a globally hyperbolic space-time from a causal set which faithfully embeds into it at sufficiently high sprinkling density. This implies a discrete-continuum correspondence which lends support to the fundamental conjecture or “Hauptvermutung” of causal set theory.
Citation Information
Major, Seth; Rideout, D.; and Surya, S., "On recovering continuum topology from a causal set" (2007). Hamilton Digital Commons.
https://digitalcommons.hamilton.edu/articles/179
Hamilton Areas of Study
Physics