%0 Journal Article %T Galilei invariant theories. I. Constructions of indecomposable finite-dimensional representations of the homogeneous Galilei group: directly and via contractions %A M. de Montigny %A J. Niederle %A A. G. Nikitin %J Mathematics %D 2006 %I arXiv %R 10.1088/0305-4470/39/29/026 %X 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. %U http://arxiv.org/abs/math-ph/0604002v1