Using explicit tetrads for any given metric and Fock–Ivanenko coefficients of the generally covariant Dirac equation, we develop a formal method to relate the wave function in a noninertial frame to that in the inertial frame. The resulting equivalence transformations are exact. The familiar cases of the rotating frame and generalized hyperbolic motion are given as examples.

Starting with the generally covariant Dirac equation we give equations showing that the spin of the Dirac particle couples directly with the background gravitational field. By restricting the metric to one describing a general 3-space metric (no gravitation) we reduce the spin-covariant Dirac equation to a two-component theory. Finally, the general form for the Pauli–Schrödinger equation is derived for any 3-space orthogonal curvilinear system of coordinates.