A Nonperturbation Approach to Quantum Electrodynamics

The equations governing the interaction of an electron with the electromagnetic fields are used in the form given by Schwinger to derive a linear integral equation for the function Γ, whose kernel is expressed as a power series in α. The first approximation to this kernel is used and the resulting integral equation solved without recourse to perturbation theory. With the aid of the solution first approximations can be found for self-energy effects, which are now finite, and some discussion of the analytic behavior of these and related quantities is given. An application of the method to meson theory illustrates the classification of the types of integral equation which arise. The possibility of extending the method is discussed.