Discrete Spacetime: a Web of Chains

Abstract

This paper studies the distribution of chain and maximal chain lengths in a causal set. We first provide a new derivation for these distributions for a causal set uniformly embedded in Minkowski space, for various dimensionalities, which includes a correction to previously available expressions. Results of numerical simulations show a better agreement with the improved theoretical distributions. As examples of applications of those distributions, we then expand on previous work of ours regarding their use in establishing whether a causal set is manifoldlike and, if it is, finding its dimensionality. We then compare this measure of the dimension with other methods in the literature.

arXiv comment26 pages, 16 figures

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Cited by in corpus (3)

• The causal set approach to quantum gravity
• Manifold Properties from Causal Sets using Chains
• A Tale of Two Actions: A Variational Principle for Two-Dimensional Causal Sets