Spectral functions from the real-time functional renormalization group

TL;DR

This paper develops a real-time functional renormalization group method on the Schwinger-Keldysh contour to compute spectral functions in scalar field theories, offering a detailed formalism, numerical approach, and benchmarking against other methods.

Contribution

It introduces a novel real-time FRG formalism on the Schwinger-Keldysh contour with specific truncation schemes and numerical procedures for spectral function calculations.

Findings

Successful computation of spectral functions in scalar theories

Comparison with perturbative and non-perturbative methods

Benchmark results in 0+1 dimensions

Abstract

We employ the functional renormalization group approach formulated on the Schwinger-Keldysh contour to calculate real-time correlation functions in scalar field theories. We provide a detailed description of the formalism, discuss suitable truncation schemes for real-time calculations as well as the numerical procedure to self-consistently solve the flow equations for the spectral function. Subsequently, we discuss the relations to other perturbative and non-perturbative approaches to calculate spectral functions, and present a detailed comparison and benchmark in $d=0+1$ dimensions.