Gravity within the Framework of Nonassociative Geometry

摘要

Recently we proposed a new mathematical theory, nonassociative geometry, providing a unified algebraic description of continuous and discrete spacetiine. It follows from our approach that nonassociativity is an algebraic equivalent of curvature and at distances comparable with Planck length the standard concept of spacetiine might be replaced by the nonassociative discrete structure, which at large spacetime scales "looks like'" a differentiable manifold. We give an up-to-date perspective with a general overview of the nonassociative geometry, a description of some discrete models of spacetiine, their continuum limit, and the emerged causal structure.