Abstract
The general problem concerning collisions is to find the probabilities of various possible final states (other assemblies of free particles) for a given initial state of the system (an assembly of free particles). This chapter discusses how the state of polarization of the particles concerned in the reaction is taken into account when calculating the scattering cross-section. It presents some kinematic relations for scattering processes in which there are only two particles, in the initial state and in the final state. The relations in question are deduced from the general conservation laws and are valid for all particles and all laws of interaction. In the helicity amplitudes, a particular frame of reference is used, namely, the centre-of-mass system. However, to calculate the scattering amplitudes by means of invariant perturbation theory and to examine their general analytical properties, it is convenient to write them in an explicitly invariant form. If the particles concerned in the reaction have no spin, the scattering amplitude depends on the invariant products of the 4-momenta of the particles.
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