  Using computer-algebraic methods we derive compact analytical expressions for
the virtual electroweak radiative corrections to polarized Compton scattering.
Moreover the helicity amplitudes for double Compton scattering, which prove to
be extremely simple in terms of Weyl-van der Waerden spinor products, are
presented for massless electrons. The inclusion of a finite electron mass is
described, too. Finally numerical results both for the purely photonic and the
full O(alpha) electroweak corrections, which turn out to be of the order of
5-10%, are discussed for energies ranging from 10GeV to 2TeV.
