The transformation behavior of ψ components is well-defined only under transitions between Cartesian axes at a point, not under arbitrary coordinate transformations.

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 bel