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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 10 GeV to 2 TeV.
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