On Einstein's unified theory

Santaló, Lluís
First, we obtain the most general tensor Tij; of rank 2 in a space with a nonsymmetrical affine connection which satisfies the following conditions: (a) it depends on the connection and its partial derivatives of the first order; (b) as a function of the connection it is, at most, of second degree. With Tij and a nonsymmetrical tensor gij; we form the classical scalar density Tij gij |g|1/2 and deduce the field equations from the corresponding variational principle. The equations are complicated, but they may be expressed in a simple way by introducing two new connections. Second, we investigate the necessary assumptions on Tij ; in order that the field equations take the simplest form compatible with the nature of the problem. This form turns out to be that of the weak system of Einstein’s unified theory of 1950, In particular, the simplifications induced by the assumptions of y-invariance and pseudo-Hermitian symmetry are investigated ​
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