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Geoffrey Dixon

Publications and source records attributed to Geoffrey Dixon.

13 recordsLinked to original sources
arXiv2014

Seeable matter; unseeable antimatter

The universe we see gives every sign of being composed of matter. This is considered a major unsolved problem in theoretical physics. Using the mathematical modeling based on the algebra ${\bf{T}} := {\bf{C}}\otimes{\bf{H}}\otimes{\bf{O}}$, an interpretation is developed that suggests that this seeable universe is not the whole universe; there is an unseeable part of the universe composed of antimatter galaxies and stuff, and an extra 6 dimensions of space (also unseeable) linking the matter side to the antimatter - at the very least.

physics.gen-ph↗
arXiv1996

Octonion X,Y-Product $G_{2}$ Variants

The automorphism group $G_{2}$ of the octonions changes when octonion X,Y-product variants are used. I present here a general solution for how to go from $G_{2}$ to its X,Y-product variant.

hep-th↗
arXiv1995

OCTONIONS: INVARIANT REPRESENTATION OF THE LEECH LATTICE

The Leech lattice, $Λ_{24}$, is represented on the space of octonionic 3-vectors. It is built from two octonionic representations of $E_{8}$, and is reached via $Λ_{16}$. It is invariant under the octonion index cycling and doubling maps.

hep-th↗
arXiv1995

OCTONION XY-PRODUCT

The octonion X-product changes the octonion multiplication table, but does not change the role of the identity. The octonion XY-product is very similar, but shifts the identity as well. This will be of interest to those applying th octonions to string theory.

hep-th↗
arXiv1995

OCTONIONS: E_{8} LATTICE TO Λ_{16}

I present here another example of a lattice fibration, a discrete version of the highest dimensional Hopf fibration: $S^{7}\longrightarrow S^{15} \longrightarrow S^{8}$.

hep-th↗
arXiv1994

Octonion X-Product and E8 Lattices

In this episode, it is shown how the octonion X-product is related to E8 lattices, integral domains, sphere fibrations, and other neat stuff.

hep-th↗
arXiv1994

Octonion X-product orbits

The octonionic X-product gives the octonions a flexibility not found in the other real division algebras. The pattern of that flexibility is investigated here.

hep-th↗
arXiv1993

Division Algebras, (1,9)-Space-Time, Matter-Antimatter Mixing

The tensor product of the division algebras, which is a kernel for the structure of the Standard Model, is also a root for the Clifford algebra of (1,9)-space-time. A conventional Dirac Lagrangian, employing the (1,9)-Dirac operator acting on the Standard Model hyperfield, gives rise to matter into antimatter transitions not mediated by any gauge field. These transitions are eliminated by restricting the dependencies of the components of the hyperfield on the extra six dimensions, which appear in this context as a complex triple.

hep-th↗
arXiv1993

Division algebras, Galois fields, quadratic residues

Intended for mathematical physicists interested in applications of the division algebras to physics, this article highlights some of their more elegant properties with connections to the theories of Galois fields and quadratic residues.

hep-th↗