T. Radozycki et I. Bialynickibirula, FINITE NONPERTURBATIVE SOLUTIONS OF DYSON-SCHWINGER EQUATIONS IN QED IN THE INFRARED DOMAIN, Physical review. D. Particles and fields, 52(4), 1995, pp. 2439-2445
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 nonperturbativ
e results obtained in this way are in agreement with perturbation theo
ry. In our approach the loop integrals are finite. Our procedure is se
lf-consistent, no divergences arise during calculations, and only a fi
nite renormalization has to be carried out.