Non-perturbative scaling in the scalar theory

TL;DR

This paper introduces a novel method to analyze the non-perturbative scaling behavior of scalar theories near the Gaussian fixed point using Green's functions, exploring conditions for generating non-polynomial interactions through the renormalization group flow.

Contribution

It presents a new approach employing Green's functions to study non-perturbative scaling and the emergence of non-polynomial interactions in scalar theories.

Findings

Identifies conditions under which non-polynomial relevant interactions are generated.

Provides explicit analysis of the scalar theory's behavior near the Gaussian fixed point.

Introduces a framework for studying non-perturbative effects in scalar field theories.

Abstract

A new approach to study the scaling behavior of the scalar theory near the Gaussian fixed point in $d$-dimensions is presented. For a class of initial data an explicit use of the Green's function of the evolution equation is made. It is thus discussed under which conditions non-polynomial relevant interactions can be generated by the renormalization group flow.