Finite nonperturbative solutions of Dyson-Schwinger equations in QED in the infrared domain

Assuming an ansatz for the vertex function and the electron propagator suggested by the Ward identity we solve the Dyson-Schwinger equations in quantum electrodynamics in the infrared domain. The nonperturbative results obtained in this way are in agreement with perturbation theory. In our approach the loop integrals are finite. Our procedure is self-consistent, no divergences arise during calculations, and only a finite renormalization has to be carried out.