In Einstein's theory of gravitation one may consider either the metric potentials $g_{\mathrm{ik}}$, or both the metric potentials and the components of the affine connection, as independent quantities (metric vs. mixed theory) in the coupling of gravitational and electronic fields. This makes a difference for the ensuing equations, but one that can be easily straightened out by a slight change of the Lagrangian; see the Theorem at the end of the paper.

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