Abstract
A unified field theory is constructed on the principle of the equivalence of mass and curvature. A salient feature of the theory is that the scalar curvature R of space-time satisfies the nonlinear wave equation D/sup 7/Alembertian/sup 2/R - a/sup -2/R = vertical-barD/sup 7/AlembertianRvertical-bar/sup 2//R. Here the new universal constant a plays the role of a fundamental length in the geometry. A solution, correct to the first order in curvature, of the field equations corresponding to static spherical symmetry is obtained by Picard's method of successive approximations. This solution is found to be free from singularities in both its gravitational and its electromagnetic parts. A consequence of this regularity is the emergence of formulas for mass and charge in terms of curvature. The prediction by the theory of the charge distribution of a particle provides a means by which the theory can be tested. For purposes of illustration, the results obtained are tentatively applied to the pion. This calculation indicates that the fundamental length a is on the order of 10/sup -13/ cm. It is concluded that a pure field theory of matter can describe in a satisfactory manner the phenomenon of an isolated particle.
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