Vector parametrization of the Lorentz group and relativistic kinematics

It is shown that by means of a complex vector parametrization of the Lorentz group it is possible to solve very simply a number of fundamental problems of relativistic kinematics, in particular, the determination of the parameters of “Wigner rotation”, the determination of the change in spin state under an arbitrary Lorentz transformation, and the classification by spin state of a system of two arbitrary scattering particles.