  The Thomas-Bargmann-Michel-Telegdi (T-BMT) equation is derived using the
Exact Foldy-Wouthuysen transformation. Extra new terms were found, and we
discuss their possible physical applications. The main point of this work is to
detail the procedure to get the general result. We explicitly present the
choice of parametrization we used on the initial Hamiltonian and the
motivations to take it. We emphasize that the final equations can depend on
this choice, and it is possible to prevent the manipulations of the quadratic
Hamiltonian become extremely cumbersome. More importantly, it is done in such a
way that the transformed equations allow the direct separation into mass,
kinetic, and interaction correction terms to the original T-BMT equation.
