A sequential growth dynamics for a directed acyclic dyadic graph

Abstract

A model of discrete spacetime on a microscopic level is considered. It is a directed acyclic dyadic graph. This is the particular case of a causal set. The goal of this model is to describe particles as some repetitive symmetrical self-organized structures of the graph without any reference to continuous spacetime. The dynamics of the model is considered. This dynamics is stochastic sequential additions of new vertexes. Growth of the graph is a Markovian process. This dynamics is a consequence of a causality principle.

21 pages, 5 figures. arXiv admin note: text overlap with arXiv:1106.6269

References in corpus (8)

• The causal set approach to quantum gravity
• Causal Sets: Discrete Gravity (Notes for the Valdivia Summer School)
• Particle propagators on discrete spacetime
• Scalar Field Theory on a Causal Set in Histories Form
• Dynamics for causal sets with matter fields: A Lagrangian-based approach
• Discrete mechanics: a sequential growth dynamics for causal sets, and a self-organization of particles
• Discrete mechanics: a kinematics for a particular case of causal sets
• Discrete mechanics: a sequential growth dynamics for causal sets that is based on binary alternatives