Generalised Local Extra Dimensions as a Basis for the Elementary Structure of Matter

A central aim of theoretical physics is to account for the structure of matter at the most elementary level as underlying the Standard Model of particle physics, and ideally also as a basis for a substantial dark sector, as distributed in 4-dimensional spacetime. A broad class of theories augment the global 4-dimensional spacetime arena itself to a higher-dimensional spacetime structure, with the properties of matter then deriving from the properties of the extra spatial dimensions. We motivate an alternative approach in which we begin with the local structure of 4-dimensional spacetime and augment the local form for a proper time interval. The symmetries and properties of the residual components, over the local 4-dimensional spacetime form, are found to exhibit appropriate features to account for the visible Standard Model sector while in parallel direct connections can also be identified with dark sector models.