Poincaré invariant differential equations for particles of arbitrary spin

Differential equations of first and second order describing the motion of a relativistic particle with arbitrary spin are derived. These equations provide the basis for an exact solution of the problem of the motion of a particle of arbitrary spin in a homogeneous magnetic field. Covariant operators for the coordinate and spin of the particle are found, and these differ from the well-known Newton–Wigner and Foldy–Wouthuysen operators. The Hamiltonian of a particle interacting with an external electromagnetic field is approximately diagonalized.