Nonlinear and spin effects in two-photon annihilation of a fermion pair in an intensive laser wave

Abstract

The pattern of calculation of amplitudes of a series of processes in the field of an intensive laser wave, in which two fermions $(p; p')$ and two real photons $(k_1; k_2)$ participate, is considered. In relation to one-photon processes, these processes are of the second order on $α$, if the wave intensity $ξ\ll 1$ (i.e., actually absorption from the wave only one quantum). Otherwise, they are competing and essentially nonlinear. One-photon processes have a number of the important physical applications. For example, $γe$ and $γγ$ colliders work on their basis. In DSB the calculation is conducted at the level of reaction amplitudes. It essentially simplifies both the calculation and the form of obtained results; those combinations of amplitudes which describe the spin effects are easy to calculate. And these effects are especially essential in nonlinear processes. The calculations are conducted in covariant form. Besides compactness, this provides independence of the frames of reference and energy modes. The masses of fermions are taken into account precisely and are not assumed equal each other (heavy leptons, modes of various decays). The pattern of calculation is given in the channel indicated in the title. The amplitudes of this channel are also applicable for calculating of induced decay of orthopositronium into two photons. And in this approach there is no necessity to assume the relative momentum equal to zero.