Generic scaling relation in the scalar $\phi^{4}$ model

TL;DR

This paper rigorously analyzes the one-loop spectrum of anomalous dimensions in the scalar 4 model, revealing a hierarchical structure and limit points, with implications for nonperturbative phenomena and other field theories.

Contribution

It provides a rigorous constructive proof of the hierarchical structure of the anomalous dimension spectrum in the 4 model, a novel insight in quantum field theory.

Findings

Naive sum of two anomalous dimensions generates a limit point in the spectrum

The spectrum exhibits a hierarchical structure

Results suggest nonperturbative characteristics and potential generalizations

Abstract

The results of analysis of the one--loop spectrum of anomalous dimensions of composite operators in the scalar $ \phi^{4} $ model are presented. We give the rigorous constructive proof of the hypothesis on the hierarchical structure of the spectrum of anomalous dimensions -- the naive sum of any two anomalous dimensions generates a limit point in the spectrum. Arguments in favor of the nonperturbative character of this result and the possible ways of a generalization to other field theories are briefly discussed.