Geodesic multiplication as a tool for classical and quantum gravity

TL;DR

This paper explores the use of algebraic structures called local geodesic loops and their tangent Akivis algebras to model classical and quantum gravity, proposing quantum conditions for infinitesimal events.

Contribution

It introduces a novel algebraic framework involving local geodesic loops and Akivis algebras for gravity theories, including quantum conditions for infinitesimal events.

Findings

Proposes local geodesic loops as models for gravity

Introduces quantum conditions for infinitesimal quantum events

Suggests algebraic structures for classical and quantum gravity

Abstract

Algebraic systems called the local geodesic loops and their tangent Akivis algebras are considered. Their possible role in theory of gravity is considered. Quantum conditions for the infinitesimal quantum events are proposed.