No abstract

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.

A special class of Dirac-Pauli equations with time-like vector potentials of an external field is investigated.\ud An exactly solvable relativistic model describing the anomalous interaction of a neutral Dirac fermion with a\ud cylindrically symmetric external electromagnetic field is presented. The related external field is a superposition\ud of the electric field generated by a charged infinite filament and the magnetic field generated by a straight line\ud current. In the nonrelativistic approximation the considered model is reduced to the integrable Pron’ko-Stroganov\ud model