Unification of Electromagnetism and Gravitation in the Framework of General Geometry

Abstract

A new geometry, called General geometry, is constructed. It is proven that its the most simplest special case is geometry underlying Electromagnetism. Another special case is Riemannian geometry. Action for electromagnetic field and Maxwell equations are derived from curvature function of geometry underlying Electromagnetism. It is shown that equation of motion for a particle interacting with electromagnetic field coincides exactly with equation for geodesics of geometry underlying Electromagnetism. It is also shown that Electromagnetism can not be geometrized in the framework of Riemannian geometry. Using General Geometry we propose a unified model of electromagnetism and gravitation which reproduces Electromagnetism and Gravitation and predicts that electromagnetic field is a source for gravitational field. This theory is formulated in four dimensional spacetime and does not contain additional fields.