Octonions and vacuum stability

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.