Wigner elementary particle in an external homogeneous field

A covariant Hamiltonian is proposed which permits to describe in the Heisenberg picture the motion of a Wigner elementary particle in a homogeneous electromagnetic field. More precisely, at any time, the elementary particle is in a state associated with a given irreducible representation of the Poincaré group. As a remarkable result, the spin motion is shown to be governed by the Thomas-Bargmann-Michel-Telegdi equation. Also the Galilean limit is discussed.