Spontaneous Generation of Effective Interaction in a Renormalizable Quantum Field Theory Model

We consider the theory of a massless scalar field $\phi$ with the $g\phi^3$ coupling in a six-dimensional space. We use Bogoliubov's method of quasiaverages to study the possibility of a breaking of the original scaling symmetry and of the corresponding spontaneous generation of the effective $G\phi^4$ coupling. We show that the linearized compensation equation for the form factor of this coupling has a nontrivial solution through the third-order approximation. In the same approximation, the Bethe–Salpeter equation for a massless scalar bound state of two fields $\phi$ also has a solution. Matching the values of the form factor and the scalar field mass $m$ at zero leads to a unique solution that gives a relation between the parameters of the$g \phi^3$ coupling and the parameters $G$ and $m$. We argue in favor of the stability of the nontrivial solution obtained.