  The tensor calculus is not the proper mathematical instrument to use  in translating the quantum-theoretic equations of the electron over  into the general theory of relativity. Vectors and terms  [tensors] are so constituted that the law which defines the  transformation of their components from one Cartesian set of axes to  another can be extended to the most general linear transformation, to an affine set of axes. That is not the case for quantity \(\psi\),  however; this kind of quantity belongs to a representation of the  rotation group which cannot be extended to the affine group.  Consequently we cannot introduce components of \(\psi\) relative to an  arbitrary coordinate system in general relativity as we can for the  electromagnetic potential and field strengths. We must rather  describe the metric at a point \(p\) by local Cartesian axes  \(e(a)\) instead of by the \(g_{pq}\).  The wave field has definite components  \(\psi^{+}_{1}, \psi^{+}_{2}, \psi^{-}_{1}, \psi^{-}_{2}\)  relative to such axes, and we know how they transform on transition to any other Cartesian axes in \(p\).