Article Title

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.

Hamilton Areas of Study

Physics