Finite Perturbation Theory in Quantum Electrodynamics

It is proved that no infinities appear in the power series expansion of the $S$ matrix in quantum electro-dynamics if one uses an improved perturbation procedure which is based on the following property of all renormalizable field theories. The dependence of solutions on the coupling constant has a singular part, nonanalytic at $g=0\mathrm{}$. This singular dependence must be treated exactly, whereas the remaining, nonsingular, dependence can be expanded into a power series. This power series coincides with the standard renormalized expansion. All renormalization constants in every order remain finite, provided their singular dependence on the coupling constant is treated exactly. The problem of convergence of the whole series has not been investigated.