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.

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In order to construct the quantum field theory in a curved space with no "old" infinities as the curvature tends to zero, the problem of contraction of representations of the corresponding group of motions is studied. The definitions of contraction of a local group and of its representations are given in a coordinate-free manner. The contraction of the principal continuous series of the de Sitter groups S0 0 (n, 1) to positive mass representations of both the Euclidean and Poincare groups is carried out in detail. It is shown that all positive mass continuous unitary irreducible representations of the resulting groups can be obtained by this method. For the Poincare groups the contraction procedure yields reducible representations which decompose into two non-equivalent irreducible representations.