Non-perturbative solutions of the SD equation for an Abelian gauge field   theory
  In this article we present a mechanism in which we find new non-perturbative solutions of quantum electrodynamics in four dimensions. Two non-perturbative solutions are found for approximate Schwinger-Dyson equations. The mass ratio of the three solutions (one is ordinary solution) is approximately $1:(8\pi/\alpha)^{2/3}:8\pi/\alpha$. 
T. Mogami