Product posets and causal automorphisms of the plane

The Causal Poset is Directed but not Lattice Ordered

In the causal set approach to discrete quantum gravity the universe grows one element at a time in discrete steps. At each step the process has the form of a causal set (causet) and the "completed" universe is given by a path through a discretely growing chain of causets. The collection of causets forms a partially ordered set (poset) in a natural way. We first show that this poset is directed. We then give a counterexample which shows it is not lattice ordered.

Causal Set Topology

The Causal Set Theory (CST) approach to quantum gravity is motivated by the observation that, associated with any causal spacetime (M,g) is a poset (M,<), with the order relation < corresponding to the spacetime causal relation. Spacetime in CST is assumed to have a fundamental atomicity or discreteness, and is replaced by a locally finite poset, the causal set. In order to obtain a well defined continuum approximation, the causal set must possess the requisite intrinsic topological and geometric properties that characterise a continuum spacetime in the large. The continuum approximation thus …

通过连续偏序集构建时空：旧基础与新发展

Spacetimes via Continuous posets: Old foundations and new developments

本文介绍连续偏序集的时空几何方法，补充相关证明并获新结果，提出拓扑Kronheimer-Penrose因果空间概念，证明相关完备化等价性，建议时空本质为余连续偏序集。

A characterization of causal automorphisms on two-dimensional Minkowski spacetime

It is shown that causal automorphisms on two-dimensional Minkowski spacetime can be characterized by the invariance of the wave equations.

A characterization of causal automorphisms by wave equations

A characterization of causal automorphism on Minkowski spacetime is given by use of wave equation. The result shows that causal analysis of spacetime may be replaced by studies of wave equation on manifolds.

The group of causal automorphisms

The group of causal automorphisms on Minkowski space-time is given and its structure is analyzed.