Functional Renormalization Analytically Continued

TL;DR

This paper presents a method for analytically continuing functional renormalization group equations from imaginary to real frequencies, enabling direct computation of real-time properties like particle decay widths in a Lorentz-invariant framework.

Contribution

It introduces a novel formalism for analytic continuation of FRG equations, allowing for self-consistent real-time analysis within a Lorentz-invariant setting.

Findings

Derived flow equations for real-time properties.

Achieved a Lorentz-invariant analytic continuation.

Enabled computation of particle decay widths.

Abstract

We discuss a method to analytically continue functional renormalization group equations from imaginary Matsubara frequencies to the real frequency axis. In this formalism, we investigate the analytic structure of the flowing action and the propagator for a theory of scalar fields with $O(N)$ symmetry. We go on to show how it is possible to derive and solve flow equations for real-time properties such as particle decay widths. Our treatment is fully Lorentz-invariant and enables an improved, self-consistent derivative expansion in Minkowski space.