On the photon Green's function

An expression is found for the photon Green's function that has the correct analytic properties and is suitable not only in the asymptotic region (see [1]) but also at small momenta. Its difference from the ordinary expression in the region of momenta $q^2\ll m^2\exp(3\pi/\alpha)$ is given by exponentially small terms of order $\exp(-3\pi/\alpha)$.