Models of the Universe based on Jordan algebras
Abstract
We propose a model for the universe based on Jordan algebras. The action consists of cubic terms with coefficients being the structure constants of a Jordan algebra. Coupling constants only enter the theory via symmetry breaking which also selects a physical vacuum. "Before" the symmetry breaking the universe is in a pre-geometric state where it makes no sense to talk about space or time, but time comes into existence with the symmetry breaking together with a Hamiltonian which can create space from "nothing" and in some cases can propagate the space to macroscopic size in a finite time. There exists symmetry breaking which results in macroscopic spacetime dimensions 3, 4, 6 and 10, based on the Jordan algebras of Hermitian 3x3 matrices with real, complex, quarternion and octonion entries,respectively.
Keywords
Cite
@article{arxiv.2003.13527,
title = {Models of the Universe based on Jordan algebras},
author = {Jan Ambjorn and Yoshiyuki Watabiki},
journal= {arXiv preprint arXiv:2003.13527},
year = {2020}
}
Comments
61 pages, 6 figures