An effective interaction spontaneously arising in a renormalizable model of quantum field theory

Abstract

Theory of massless scalar field $\varphi$ with interaction $g{\varphi }^3$ in six-dimensional space is considered. A possibility of initial scale invariance breaking, which results in a spontaneous arising of effective interaction $G{\varphi }^4$, is studied by application of Bogolubov quasi-averages approach. It is shown, that compensation equation for form-factor of this interaction in approximation up to the third order in $G$ has a non-trivial solution. The conditions imposed on form-factor value at zero and scalar field mass $m$ fix the unique solution, which gives relations between parameters of interaction $g{\varphi }^3$ and parameters $G$ and $m$. Arguments are laid down in favour of a stability of the non-trivial solution.

21 pages, 2 figures