On the “false” pole of the photon Green's function

The paper contains the results of the application of a differential method (differential in the coupling constant) to the theory of boson-fermion three-particle interaction and, in particular, quantum electrodynamics. An expression is obtained for the photon Green's ffmction with the correct analytic properties in any finite part of the complex plane of the energy and the square of the momentum; this expression has a nonanalytic dependence on the coupling constant and goes over into the usual solution if an expansion is made in a perturbation theory series.