Summary of a non-uniqueness problem of the covariant Dirac theory and of two solutions of it

We present a summary of: 1) the non-uniqueness problem of the Hamiltonian and energy operators associated, in any given coordinate system, with the generally-covariant Dirac equation; 2) two different ways to restrict the gauge freedom so as to solve that problem; 3) the application of these two ways to the case of a uniformly rotating reference frame in Minkowski spacetime: we find that a spin-rotation coupling term is there only with one of these two ways.