Non-Perturbative Renormalization Group calculation of the scalar self-energy

TL;DR

This paper introduces a numerical method for solving non-perturbative renormalization group equations to compute n-point functions with full momentum dependence, demonstrated through scalar self-energy calculations at criticality.

Contribution

It presents a new numerical approach to solve non-perturbative RG equations for n-point functions, including their momentum dependence, with accuracy comparable to derivative expansion methods.

Findings

Accurate calculation of scalar self-energy across all momenta.

Method is computationally comparable to derivative expansion.

First numerical application of this RG approach to n-point functions.

Abstract

We present the first numerical application of a method that we have recently proposed to solve the Non Perturbative Renormalization Group equations and obtain the n-point functions for arbitrary external momenta. This method leads to flow equations for the n-point functions which are also differential equations with respect to a constant background field. This makes them, a priori, difficult to solve. However, we demonstrate in this paper that, within a simple approximation which turns out to be quite accurate, the solution of these flow equations is not more complicated than that of the flow equations obtained in the derivative expansion. Thus, with a numerical effort comparable to that involved in the derivative expansion, we can get the full momentum dependence of the n-point functions. The method is applied, in its leading order, to the calculation of the self-energy in a 3-dimensional scalar field theory, at criticality. Accurate results are obtained over the entire range of momenta.