Green's functions in broken discrete symmetry

Abstract

Scalar fields with interaction

$$\begin{array}{*{20}c} {\lambda \sum\limits_{i \ne j} {\phi i^2 \phi j^2 } } & {or} & {\lambda '\sum\limits_{i,j,k,l pairwise disticnt} {\phi i\phi j\phi k\phi l} } \\ \end{array} $$

are considered in Green's function formalism of quantum field theory. Equations for Green's functions are derived under the assumption that someG _2n+1 are not zero. Descending problems from given (modelG ₃,G ₄ and fromG ₄,G ₅ are discussed, without appealing to perturbation theory.