Integral Equations of Quantized Field Theory

Abstract

A systematic method is developed for the solution of the integral equations of quantized field theory. It is first shown how to generalized these equations for any number of fermions in interaction with a boson field, and then how to apply the renormalization procedure to the resulting equations. A method of approximation to the solution of the "renormalized" equations is described, which yields divergence-free covariant scattering amplitudes, analogous to the Tamm-Dancoff amplitudes. It is shown that the $n\mathrm{th}$ order Tamm-Dancoff amplitudes do not approach limiting values for large $n$, and that the procedure does not therefore converge; but that a somewhat modified procedure would probably do so. Singularities in the scattering amplitudes, regarded as functions of the coupling constant, are related to the existence of bound states.