Green's functions in an exterior gauge field

We consider the problem of evaluating the fermion Green's functions in an exterior Abelian-like gauge field. It is shown that in the field considered, the fermion Green's functions are expressed in terms of spinor particle Green's functions in some exterior electromagnetic field. The Green's functions are found in a combination of a constant homogeneous field and a plane wave field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 67–70, September, 1987.In conclusion the authors wish to express thanks to V. G. Bagrov and D. M. Gitman for helpful discussions of the problems touched upon in the article.