In the preface of Lawson & Michelsohn's Spin Geometry, they mentioned some physics relevant to their book which I find interesting:
The theory of Dirac had another interesting feature. In the presence of an electromagnetic field the Dirac Hamiltonian contained an additional term added on to what one might expect from the classical case. There were strong formal analogies with the additional term one obtains by introducing internal spin into the mechanical equations of an orbiting particle.
I don't know any quantum mechanics but I was once a student in mechanical engineering, so I want to at least understand one side of the analogies so that I could probably better understand the math. Could someone explain these analogies in more details? In particular, could you write down the "mechanical equation" and the additional "internal spin" term?