  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.
