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 $1:(8\pi \mathrm{/}\alpha {)}^{2\mathrm{/}3}:8\pi \mathrm{/}\alpha$.