Descending problem in Green's function approach to quantum field theory

Abstract

The question how to determine lower many-point functions in terms of higher ones, which we call the descending problem, is discussed for the (ø4)1+3 model of quantum field theory. Equations to be considered are non-linear non-compact operator equations in complex Banach spaces. Several sufficient sets of conditions for convergence of successive approximation schemes are presented for small values of the renormalised coupling constant. Local uniqueness of solution is proved under certain conditions.