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

Boris A. Arbuzov
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Abstract

Theory of massless scalar field $ϕ$ with interaction $g ϕ^3$ in six-dimensional space is considered. A possibility of initial scale invariance breaking, which results in a spontaneous arising of effective interaction $G ϕ^4$, 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 $g ϕ^3$ and parameters $G $ and $m$. Arguments are laid down in favour of a stability of the non-trivial solution.

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Boris A. Arbuzov. 2004-02-17. An effective interaction spontaneously arising in a renormalizable model of quantum field theory. https://arxiv.org/abs/hep-th/0401154

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