6 papers · 1 filter
(1,9)-spacetime --> (1,3)-spacetime: Reduction => U(1)xSU(2)xSU(3)
Geoffrey Dixon
A derivation of the standard symmetry and leptoquark family structure is presented that is more straightforward than a previous derivation.
Division Algebras: 26 Dimensions; 3 Families
Geoffrey Dixon
The link of the Division Algebras to 10-dimensional spacetime and one leptoquark family is extended to 26-dimensional spacetime and three leptoquark families.
OCTONIONS: INVARIANT LEECH LATTICE EXPOSED
Geoffrey Dixon
The structure of a previously developed representation of the Leech lattice, , is exposed to further light with this unified and very simple construction.
OCTONIONS: INVARIANT REPRESENTATION OF THE LEECH LATTICE
Geoffrey Dixon
The Leech lattice, , is represented on the space of octonionic 3-vectors. It is built from two octonionic representations of , and is reached via . It is inv…
Octonion X-Product and E8 Lattices
Geoffrey Dixon
In this episode, it is shown how the octonion X-product is related to E8 lattices, integral domains, sphere fibrations, and other neat stuff.
Division Algebras, (1,9)-Space-Time, Matter-Antimatter Mixing
Geoffrey Dixon
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…