On the possibility of dynamical mass generation in finite quantum electrodynamics

Solution of nonlinear integral equation for the mass operator is constructed in the framework of the “finite” quantum electrodynamics by Johnson et al. with the vanishing bare mass. The study aims to solve the problem of possiblle existence of the massive solution of the equation, i.e. the problem of dynamical mass generation. It is shown that at positive values of the bare coupling constant $\alpha_0>0$, there is no physically reasonable solution of the equation due to the presence of the complex singularities in the $p^2$-plane. At negative $\alpha_0$ the solutions possess the analytical properties desired, but they increase with the growth of $p^2$ which produces the divergences in the integral equation. The main conclusion which is drawn is that the dynamical mass generation does not take place in the finite quantum electrodynamics at any values of $\alpha_0$.