CONSTRUCTION THEORY OF THE INHOMOGENEOUS LORENTZ GROUP AS FUNDAMENTALS OF QUANTUM MECHANICAL KINEMATICS

The construction of the inhomogeneous Lorentz group is discussed from the viewpoint of relativistic kinematics, within the limitations of the construction with the characteristic invariants P/sub mu P/sup mu > 0. The construction given depends essentially on an explicit calculation of Wigner considerations. The problem of reducing this construction of the homogeneous Lorentz group is solved, explicitly for the construction of the inhomogeneous group, by a transformation from the canonical basis to another basis into which the construction operators of the homogeneous Lorentz transformation is decomposed. The analogs to the Clebsch-Gordon series for the product construction of the rotational group were determined for the product of the two irreducible constructions of the inhomogeneous Lorentz group. (J.S.R.)