Nonassociative geometry: Towards discrete structure of spacetime

TL;DR

This paper proposes a nonassociative geometric framework that unifies continuum and discrete spacetime descriptions, introducing a diodular discrete structure that approximates a smooth manifold at large scales.

Contribution

It introduces a novel nonassociative geometric approach to model spacetime as a diodular discrete structure, bridging discrete and continuum descriptions.

Findings

Diodular discrete structures approximate smooth manifolds at large scales.

Nonassociative geometry provides a unified description of continuum and discrete spacetime.

Application to nonassociative de Sitter spacetimes demonstrates the framework's potential.

Abstract

In the framework of nonassociative geometry (hep-th/0003238) a unified description of continuum and discrete spacetime is proposed. In our approach at the Planck scales the spacetime is described as a so-called "diodular discrete structure" which at large spacetime scales `looks like' a differentiable manifold. After a brief review of foundations of nonassociative geometry,we discuss the nonassociative smooth and discrete de Sitter spacetimes.