Quantum of area from gravitation on complex octonions

Abstract

Using spin 1/2 particle elastic scattering on a fixed target, in a 1/|x| potential on Euclidean metric, a minimum scattering cross section appears from the spin contribution. Interpreted as semi-classical limit of an earlier proposed operator formulation of four dimensional Euclidean quantum gravity, using non-associative complex octonion algebra, this is understood as an area quantum for the observation: Existence of finite (quantized) charges yields a minimum area element of interaction. This suggests that models built on the fundamental assumption of a quantized area element (namely as in Loop Quantum Gravity) may in principle approximate General Relativity in the non-quantum limit.