  This article is devoted problems of electromagnetic interaction in curved
spacetime. Such problems exist, in particular, when we investigate
electromagnetic quantum processes near black holes. The generalization of
reduction formalism permits to find formulas for scattering matrices. For the
free Dirac and electromagnetic fields corresponding generating functionals are
calculated. Next we have found the generating functional for the interaction of
these fields. This result holds the central position in our investigation. By
means of generating functionals and reduction formulas we have obtained the
scattering amplitudes for elementary electrodynamic processes: Compton
scattering and the annihilation of electron-positron pair (for the tree-level
approximation). On the base of these results we have formulated the generalized
Feynman rules for the electromagnetic interaction in curved spacetime. Another
electrodynamic processes can be studied by means of these Feynman rules and
crossing-symmetry. The generating functional can be used to study problems of
quantum statistics in curved spacetime.
