The spectrum of the anomalous dimensions of the composite operators in the $\epsilon$ - expansion in the scalar $\phi^4$ - field theory

TL;DR

This paper analyzes the spectrum of anomalous dimensions of composite operators in scalar ^4 theory using -expansion, providing exact solutions for small operators and insights into large derivative limits.

Contribution

It offers the first exact solutions for operators with up to four fields and explores the spectrum's structure for arbitrary operator size in -expansion.

Findings

Exact solutions for operators with    4 fields

Behavior of anomalous dimensions at large derivatives

Qualitative spectrum structure for arbitrary n

Abstract

The spectrum of the anomalous dimensions of the composite operators (with arbitrary number of fields $n$ and derivatives $l$) in the scalar $\phi^4$ - theory in the first order of the $\epsilon$ -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 $n$.