Galilei invariant theories. I. Constructions of indecomposable   finite-dimensional representations of the homogeneous Galilei group: directly   and via contractions
  All indecomposable finite-dimensional representations of the homogeneous Galilei group which when restricted to the rotation subgroup are decomposed to spin 0, 1/2 and 1 representations are constructed and classified. These representations are also obtained via contractions of the corresponding representations of the Lorentz group. Finally the obtained representations are used to derive a general Pauli anomalous interaction term and Darwin and spin-orbit couplings of a Galilean particle interacting with an external electric field. 
M. de Montigny, J. Niederle and A.G. Nikitin