Gravitation and electromagnetism in theory of a unified four-vector field

Abstract

A four-vector field in flat space-time, satisfying a gauge-invariant set of second-order differential equations, is considered as a unified field. The model variational principle corresponds to the general covariance idea and gives rise to nonlinear Born-Infeld electrodynamics. Thus the four-vector field is considered as an electromagnetic potential. It is suggested that space-localized (particle) solutions of the nonlinear field model correspond to material particles. Electromagnetic and gravitational interactions between field particles appear naturally when a many-particle solution is investigated with the help of a perturbation method. The electromagnetic interaction appears in the first order in the small field of distant particles. In the second order, there is an effective Riemannian space induced by the field of distant particles. This Riemannian space can be connected with gravitation.