The spectrum of the anomalous dimensions of the composite operators in the $ε$ - expansion in the scalar $ϕ^4$ - field theory

Abstract

The spectrum of the anomalous dimensions of the composite operators (with arbitrary number of fields $n$ and derivatives $l$) in the scalar $ϕ^4$ - theory in the first order of the $ε$ -expansion is investigated. The exact solution for the operators with number of fields $\leq 4$ is presented. The behaviour of the anomalous dimensions in the large $l$ limit has been analyzed. It is given the qualitative description of the %structure of the spectrum for the arbitrary $n$.