arXiv subjects
Publications and source records attributed to Alexander I. Nesterov.
The connection between Jacobi fields and odular structures of affine manifold is established. It is shown that the Jacobi fields generate the natural geoodular structure of affinely connected manifolds.
In the framework of nonassociative geometry (hep-th/0003238) a unified description of continuum and discrete spacetime is proposed. In our approach at the Planck scales the spacetime is described as a so-called "diodular discrete structure" which at large spacetime scales `looks like' a differentiable manifold. After a brief review of foundations of nonassociative geometry,we discuss the nonassociative smooth and discrete de Sitter spacetimes.
We obtain the integral formulae for computing the tetrads and metric components in Riemann normal coordinates and Fermi coordinate system of an observer in arbitrary motion. Our approach admits essential enlarging the range of validity of these coordinates. The results obtained are applied to the geodesic deviation in the field of a weak plane gravitational wave and the computation of plane-wave metric in Fermi normal coordinates.
A description of generalized coherent states and geometric phases in the light of the general theory of smooth loops is given.
A new mathematical theory, non-associative geometry, providing a unified algebraic description of continuous and discrete spacetime, is introduced.