  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.
