Octonionic geometry and conformal transformations

TL;DR

This paper explores a novel geometric framework for space-time using split octonions and their automorphism group G2, linking it to conformal transformations in Minkowski space and providing insights into the cosmological constant.

Contribution

It introduces a model of space-time based on split octonions and G2 symmetry, connecting higher-dimensional geometry with conformal transformations and cosmological observations.

Findings

G2 automorphisms relate to conformal transformations in 4D space-time

The model naturally predicts the observed cosmological constant value

Octonionic geometry offers a new perspective on space-time structure

Abstract

We describe space-time using split octonions over the reals and use their group of automorphisms, the non-compact form of Cartan's exceptional Lie group G2, as the main geometrical group of the model. Connections of the G2-rotations of octonionic 8D space with the conformal transformations in 4D Minkowski space-time are studied. It is shown that the dimensional constant needed in these analysis naturally gives the observed value of the cosmological constant.