In this paper we present the full calculation of the final photon pola
rization in the Compton scattering on electron gamma + e --> gamma + e
. We claim to be in disagreement with some of the results quoted by ER
. Arutyunian and V.A. Tumanian in Sov. Phys. Usp. 83 (1964) 339; Phys.
Lett. 4 (1963) 177.