2019/09/02 by D. J. Jackson, Jackson, David J.
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Physical sciences #General Physics (physics.gen-ph) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.1909.05014
openalex publication_date 2019/09/02 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
In considering the nature of the basic mathematical structures appropriate for describing the fundamental elements of particle physics a significant role for the octonions, as an extension from the complex numbers and uniquely the largest division algebra, has occasionally been proposed. Rather than being based initially upon the more abstract grounds of mathematical aesthetics, here we describe a unified theory motivated conceptually through an elementary generalisation of the expression for a local proper time interval, beyond that of 4-dimensional spacetime and also beyond that of the local structure of models with extra spatial dimensions, for which the explicit mathematical development naturally incorporates the octonion algebra as an essential feature. Properties of matter are identified directly through the symmetry breaking structure entailed in the necessary extraction of the external 4-dimensional spacetime background and are shown to reproduce a series of characteristic structures of the Standard Model of particle physics. While already employing octonion-based constructions of the exceptional Lie groups E6 and E7 the uncovering of the full Standard Model, as well as new physics beyond, is predicted to involve an E8-related structure for which the octonion algebra is again anticipated to be of fundamental importance.