Convergent perturbation theory and the strong coupling limit in quantum electrodynamics

The well-known formalism for constructing a convergent quantum field perturbation theory with a finite radius of convergence is modified to obtain convergent series in quantum electrodynamics. We prove that the constructed series converge and determine the radius of convergence. The convergent quantum field perturbation theory is used to study the strong-coupling limit in quantum electrodynamics and in the $\varphi^4$ model of critical behavior. We obtain strong-coupling limits for the $\beta$-functions of the theories under study and confirm that the Landau pole in quantum electrodynamics does exist and is not an artifact of perturbation theory.