Self-consistent Spectral Functions in the $O(N)$ Model from the FRG

TL;DR

This paper introduces a novel self-consistent method within the Functional Renormalization Group framework to calculate spectral functions in the relativistic $O(N)$ model, considering full momentum dependence.

Contribution

It is the first to perform a self-consistent direct spectral function calculation in the FRG framework with full momentum dependence in the $O(N)$ model.

Findings

Successful computation of spectral functions with complex momentum dependence

Comparison between Euclidean and complex momentum spectral functions

Foundation for applying this method to more complex systems

Abstract

We present the first self-consistent direct calculation of a spectral function in the framework of the Functional Renormalization Group. The study is carried out in the relativistic $O(N)$ model, where the full momentum dependence of the propagators in the complex plane as well as momentum-dependent vertices are considered. The analysis is supplemented by a comparative study of the Euclidean momentum dependence and of the complex momentum dependence on the level of spectral functions. This work lays the groundwork for the computation of full spectral functions in more complex systems.