Crystallography, relativity and octonions

TL;DR

This paper explores how octonions can be used to extend spacetime dimensions in condensed matter models to maintain relativistic covariance, linking crystallography, relativity, and octonionic algebra.

Contribution

It proposes a novel approach of using octonions to expand spacetime dimensions for relativistic models in condensed matter physics.

Findings

Octonions provide a mathematical framework for higher-dimensional spacetime.

Expanding to an eight-dimensional tangent bundle preserves relativistic covariance.

Potential advantages of octonions in modeling fundamental interactions in condensed matter.

Abstract

In condensed matter theory many invaluable models rely on the possibility of subsuming fundamental particle interactions in constitutive relations for macroscopic fields in near equilibrium assemblies of particles. Should one wish to maintain relativistic covariance this substitution generates a problem that can only be addressed by expanding the dimension of the space-time base manifold (four) to that of its tangent bundle (eight). The linear vector space of the octonions over the real (or conceivably rational) field seem to offer definite advantages in doing this.