Analytic continuation of functional renormalization group equations

TL;DR

This paper develops a method to analytically continue functional renormalization group equations from imaginary to real frequencies, enabling the calculation of real-time properties like decay widths while preserving space-time symmetries.

Contribution

It introduces a formalism for real-time analysis within the functional renormalization group framework, maintaining symmetries and enabling self-consistent approximations.

Findings

Derived flow equations for real-time properties.

Demonstrated conservation of Lorentz and Galilei invariance.

Enabled calculation of propagator residues and decay widths.

Abstract

Functional renormalization group equations are analytically continued from imaginary Matsubara frequencies to the real frequency axis. On the example of a scalar field with O(N) symmetry we discuss the analytic structure of the flowing action and show how it is possible to derive and solve flow equations for real-time properties such as propagator residues and particle decay widths. The formalism conserves space-time symmetries such as Lorentz or Galilei invariance and allows for improved, self-consistent approximations in terms of derivative expansions in Minkowski space.