Über den Spin in der allgemeinen Relativitätstheorie: Eine notwendige Erweiterung der Einsteinschen Feldgleichungen

Abstract

In this article the problem ofgeometrizing spin-angular momentum is treated.

First we emphasize the far-reaching analogy between General Relativity and the differential geometric version of the field theory ofdislocations. Starting from this, we obtain inter alia the result that spinning matter cannot be imbedded in a four-dimensional Riemannian space, but that one needs a geometry with a non-symmetric affine connexion. From a correspondingvariational principle we then deduce field equations, which are a straightforward generalisation ofEinstein's equations of 1916.