New Possibilities for a Unified Field Theory

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Abstract
The introduction of nonsymmetric gik in unified field theories of the Einstein‐Schrödinger type is open to the objection, on group‐theoretical grounds, that the symmetric and antisymmetric parts transform independently. This objection does not apply to the use of nonsymmetric Γikμ, since these quantities are irreducible under the ``extended group,'' consisting of the point transformations and the Einstein λ transformations. We consider a theory based on symmetric gik and nonsymmetric Γikμ. The Lagrangian L is assumed to depend only on gik and the contracted curvature tensor Rik (this insures the λ invariance and transposition invariance of the theory). For simplicity, we suppose further that L involves Rik rationally and, at most, quadratically. The resulting theory is able to account satisfactorily for the main feature of gravitation, electromagnetism, and their interaction. In particular, the theory yields the correct equations of motion for charged masses. The electromagnetic tensor is associated with the skew part of Rik, and the λ transformations correspond roughly to the gauge transformations of electrodynamics.

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