The GUT of the light: On the Abelian Complexifications of the Euclidean Rn spaces
Abstract
The new great development in Physics could be related to the excited progress of a new mathematics: ternary theory of numbers, ternary Pithagor theorem and ternary complex analysis, ternary algebras and symmetries, ternary Clifford algebras,ternary differential geometry, theory of the differential wave equations of the higher degree n>2 and etc. Especially, we expect the powerful influence of this progress into the Standard Model (SM) and beyond, into high energy neutrino physics, Gravity and Cosmology. This can give the further development in the understanding of the Lorentz symmetry and matter-antimatter symmetry, the geometrical origin of the gauge symmetries of the Standard Model, of the 3-quark-lepton family and neutrino problems, dark matter and dark energy problems in Cosmology. The new ambient geometry can be related to a new space-time symmetry leading at high energies to generalization of the Special Theory of Relativity. We related the future of this development with Cn numbers, n-algebras (n>2) and corresponding geometrical objects. We will discuss the following results - Cn complexification of Rn spaces - Cn structure and the invariant surfaces - Cn holomorphicity and harmonicity - The link between Cn holomorphicity and the origin of spin 1/n - New geometry and N-ary algebras/symmetries - Root system of a new ternary TU(3) algebra - N-ary Clifford algebras - Ternary 9-plet and 27-plet number surfaces
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