Lecture 2: Merab Gogberashvili (Javakhishvili Tbilisi State University, Georgia)

Title: Geometrical Applications of Split Octonions

Geometrical applications of split octonions is considered. Eight real parameters characterizing physical signals are related to space-time coordinates, to the classical action and to the wavelengths.

Representation of rotations by split octonions (active transformations of basis units) lead to the real non-compact form of Cartan's group G2.

Elementary particles are connected with zero divisors, the elements which nullify octonionic intervals.

In front of time-like coordinates in the expression of pseudo-Euclidean intervals naturally appear two fundamental physical parameters, the light speed and Planck's constant.

From the requirement of positive definiteness of norms under G2-transformations, together with the introduction of the maximal velocity, there follow uncertainty relations.

References:

Geometry of Non-Compact G(2), J. Geom. Phys. 144 (2019) 308

Octonionic Geometry and Conformal Transformations, Int. J.Geom . Meth . Mod . Phys . 13 (2016) 1650092

Geometrical Applications of Split Octonions, Adv. Math. Phys. 2015(2015) 196708

Octonionic Electrodynamics, J. Phys. A 39 (2006) 7099

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