Real time correlation functions and the functional renormalisation group

TL;DR

This paper introduces a functional renormalisation group method for directly calculating real time correlation functions, applicable at finite temperature and density, and capable of handling complex frequencies and real time on the Keldysh contour.

Contribution

It develops a novel RG approach with symmetry-preserving regulators for real time correlation functions, bridging imaginary and real time computations.

Findings

Allows computation of correlation functions at complex frequencies

Preserves space-time symmetries with new regulators

Enables real time analysis on the Keldysh contour

Abstract

We put forward a functional renormalisation group approach for the direct computation of real time correlation functions, also applicable at finite temperature and density. We construct a general class of regulators that preserve the space-time symmetries, and allows the computation of correlation functions at complex frequencies. This includes both imaginary time and real time, and allows in particular the use of the plethora of imaginary time results for the computation of real time correlation functions. We also discuss real time computation on the Keldysh contour with general spatial momentum regulators. Both set-ups give access to the general momentum and frequency dependence of correlation functions.