Methods of Minimization of Calculations in High Energy Physics: 1. A Covariant Method of the Calculation of Amplitudes of Processes Involving Polarized Dirac Particles

The article deals with a number of the existings variants of direct calculation of amplitudes of processes with polarized Dirac particles. It is shown, that all of them are special cases of one and the same mathematical scheme. The advantages and disadvantages of this scheme are considered. A new variant of the method of calculation of amplitudes, keeping all the advantages of this scheme, but free from disadvantages, is proposed. In particular, this variant is suitable for the evaluation of amplitudes of processes with interfering diagrams and does not need any additional calculations, that are necessary in the general case. Expressions for the amplitudes of processes involving both massive and massless particles are presented. These expressions make it possible to create in an easy way the computer programs for automatic calculation of amplitudes. The existing computer programs for calculation of amplitudes, their limitations and disadvantages are briefly considered.