Octonions and vacuum stability

TL;DR

This paper explores how octonion-based Dirac matrices relate to stable vacuum states in higher-dimensional space-time, suggesting a fundamental link between internal space properties and unified interaction theories.

Contribution

It demonstrates that octonion matrix elements describe internal degrees of freedom only in stable or near-stable vacuum states, linking internal space dimensions to vacuum stability.

Findings

Octonion matrix elements correspond to stable vacuum states.

Internal space dimension matches signature in different approaches.

Octonion structures influence vacuum stability and unified theories.

Abstract

The paper addresses one of nontrivial octonion related facts. According to paper gr-qc/0409095, the most stable space-time state is the one described by real Dirac matrices in 11-dimensional space of signature 1(-)&10(+). The internal subspace is 7-dimensional, and its stability is due to a high ``zero'' energy packing density when using an oblique-angled basis from fundamental vectors of lattice E_8 for the spinor degrees of freedom. The nontrivial fact consists in the following: Dirac symbols with octonion matrix elements can be used to describe states of the space of internal degrees of freedom if and only if the space corresponds either to stable vacuum states or states close to the just mentioned ones. The coincidence of the internal space dimension and signature for absolutely different and independent approaches to the consideration of this issue seems to predetermine the internal space vacuum properties and the apparatus, which is able to constitute the basis of the unified interaction theory.