General description of Dirac spin-rotation effect with relativistic factor

Abstract

The Mashhoon rotation-spin coupling is studied by means of the parallelism description of general relativity. The relativistic rotational tetrad is exploited, which results in the Minkowski metric, and the torsion axial-vector and Dirac spin coupling will give the Mashhoon rotation-spin term. For the high speed rotating cases, the tangent velocity constructed by the angular velocity $\Ome$ multiplying the distance r may exceed over the speed of light c, i.e., $\Ome r \ge c$, which will make the relativistic factor $\gamma$ infinity or imaginary. In order to avoid this "meaningless" difficulty occurred in $\gamma$ factor, we choose to make the rotation nonuniform and position-dependent in a particular way, and then we find that the new rotation-spin coupling energy expression is consistent with the previous results in the low speed limit.