The relativity of space-time-property

We describe a geometrical way to unify gravity with the other natural forces by adding fermionic Lorentz scalar variables, characterising attribute, or property, to space-time location. [With five such properties one can accommodate all known leptons and quarks.] Using just one property, viz. electricity, the general relativity of such a scheme and its superscalar curvature automatically produces the Einstein-Maxwell Lagrangian and a cosmological term. By adding more properties we envisage the geometrical unification of the standard model with gravitation.Comment: 11 pages, conference proceeding

Matrix Representation of Octonions and Generalizations

We define a special matrix multiplication among a special subset of 2N\x 2N matrices, and study the resulting (non-associative) algebras and their subalgebras. We derive the conditions under which these algebras become alternative non-associative and when they become associative. In particular, these algebras yield special matrix representations of octonions and complex numbers; they naturally lead to the Cayley-Dickson doubling process. Our matrix representation of octonions also yields elegant insights into Dirac's equation for a free particle. A few other results and remarks arise as byproducts.Comment: 18 printed page