A general theorem on temporal foliation of causal sets

TL;DR

This paper proves a general theorem on the existence of temporal foliations in causal sets and classifies their automorphisms, which could aid in the quantization of these structures.

Contribution

It introduces a general theorem on temporal foliations in causal sets and classifies automorphisms into spacelike automorphisms or time translations.

Findings

Existence of temporal foliations under mild constraints

Automorphisms are either spacelike automorphisms or time translations

Results may facilitate quantization of causal sets

Abstract

We show a general theorem of existence of temporal foliations in a general causal set, under mild constraints. Then we study automorphisms of infinite causal sets (which satisfy further requirements) and show that they fall under one of two types: 1) Automorphims that induce automorphisms of spacelike hypersurfaces in some given foliation (i.e. spacelike automorphisms), or 2) Translation in time. These results might be useful for quantization of the aforementioned causal sets.