Motion of Particles in Einstein's Relativistic Field Theory. I. Introduction and General Theory

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Abstract
If we represent particles through singularities in the field—we shall call such particles ideal particles—the field equations of Einstein's theory of the nonsymmetric field (unified field theory) can be solved step by step with respect to the powers of a parameter which measures the "strength" of the singularities associated with each particle. In paper I we develop the above-mentioned approximation procedure and show that ideal particles in an isolated region of space-time interact with each other as if each particle were acted on by a force which depends on the particle's kinematic and structural properties and on a certain external field in the neighborhood of the particle. The approximation procedure allows one to find, to any order of approximation desired, the equations of motion satisfied by each particle, the equations of change satisfied by those quantities which characterize the structure of each particle, and the field equations satisfied by the external field which acts on each particle. The equations are Lorentz-covariant in form.