38 research outputs found
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