A manifestly covariant framework for causal set dynamics

TL;DR

This paper introduces a covariant framework for causal set dynamics using covtree, a partial order structure, establishing a connection between paths in covtree and infinite causal sets, and defining transition probabilities for classical measures.

Contribution

It presents a novel covariant framework for causal set dynamics based on covtree, linking paths to causal sets and defining classical measures via transition probabilities.

Findings

Every infinite path in covtree corresponds to an infinite causal set.

Transition probabilities induce a classical measure on stem sets.

The framework ensures manifest covariance in causal set dynamics.

Abstract

We propose a manifestly covariant framework for causal set dynamics. The framework is based on a structure, dubbed covtree, which is a partial order on certain sets of finite, unlabeled causal sets. We show that every infinite path in covtree corresponds to at least one infinite, unlabeled causal set. We show that transition probabilities for a classical random walk on covtree induce a classical measure on the $\sigma$-algebra generated by the stem sets.