Nonperturbative Green's function approach to quantum field theory and arbitrariness of solutions

Abstract

Green's function equations are considered for interacting spinor and (pseudo) scalar fields with interactions \(g\bar \psi \gamma \psi \phi + \tfrac{1}{4}\lambda \phi ^4 \). These equations do not determine higher many-point functions if two-point functions are given as “input.” If vertex parts are given as input, two-point functions are determined but higher many-point functions are not determined.