The Rich Structure of Minkowski Space

TL;DR

This paper explores the complex geometric and algebraic structures of Minkowski space, revealing its rich features beyond its simple topological and flat nature, including causality, symmetry groups, and the Noether-Herglotz theorem.

Contribution

It provides a detailed analysis of Minkowski space's structure, covering affine spaces, symmetry groups, causality lattices, and the Noether-Herglotz theorem, highlighting its intricate properties.

Findings

Detailed description of Minkowski space's affine structure

Analysis of causally complete regions and their lattices

Discussion of the Noether-Herglotz theorem in this context

Abstract

Minkowski Space is the simplest four-dimensional Lorentzian Manifold, being topologically trivial and globally flat, and hence the simplest model of spacetime--from a General-Relativistic point of view. But this does not mean that it is altogether structurally trivial. In fact, it has a very rich structure, parts of which will be spelled out in detail in this contribution. This will contain elementary aspects of affine spaces, various paths to the Poincare group, the lattices of causally and chronologically complete regions, and last but not least, the Noether-Herglotz theorem.