Partial wave analysis based on a complex vector parametrization

A partial analysis of one- and two-particle states is made on the basis of a complex vector parametrization of the Larentz group. In the given approach the transformations of the littte group are interpreted as rotations in a corresponding complex three-dimensional space of parameters of this group; this interpretation makes it possible to construct conveniently the states of a two-particle system with a definite value of the total angular momentum and its projection. This construction is used to decompose the $S$ matrix with respect to partial waves.