On matrix elements of quantum electrodynamics

Recurs ion relations are derived that yield simple and compact expressions for the traces of operators containing many Dirac matrices. It is shown that for moving particles the projection of the spin onto an arbitrary axis can have a definite value. A general relation is given for calculating the matrix elements instead of the squares of their moduli, which enables one to significantly simplify the calculation of cross sections of various processes in quantum electrodynamics, especially when the polarization of all the particles is taken into account.