Field equations and the tetrad connection Available to Purchase

A fundamental result of Geroch is that a space‐time admits a spinor structure if and only if it is parallelizable. A nonsymmetric, metric‐compatible curvature‐free connection is associated with a global orthonormal tetrad field on such a parallelizable space‐time. This connection is used to examine reported inconsistencies for S> 1/2 spinor field equations on general space‐times. It is shown that the assumed Levi–Civita transport of Clifford units causes the inconsistencies at the Klein–Gordon stage. The relation of the torsion tensor of the parallelization connection to the space‐time topology is indicated and the Lorentz covariance of the modified Klein–Gordon equations is demonstrated. A particularly simple plane‐wave solution form for free‐field equations is shown to result for locally flat space‐times for which the torsion tensor is necessarily zero.