On the motion of charged particles in the complex-symmetric unified field theory

Abstract

In the complex syinmetric unified theory the equations of motion of charged particles were derived from the field equations by an application of the Einsteim, Infeld, and Hoffman approximation method and the technique of deriving equations of motiom introduced by Infeld. These equations of motion contained the Lorentz force. However, at each stage of approximation in the general theory, the equations of motion proved to be incompatible. In the present paper it is pointed out that by taking into account the conditions of integrability of the field equations this incompatibility is removed. In the first treatment of this problem a source tensor expressed linearly in terms of the Dirac sigma - function is used. The conditions of integrability of these field equations can be taken into account---and the incompatibility removed---by applying the dipole procedure introdueed recently by Infeld and Plebanski. The new treatment is basod on the complex symmetric field equations of empty space. (A.C.)