Functional renormalisation group approach to far-from-equilibrium quantum field dynamics

TL;DR

This paper develops a non-perturbative functional renormalisation group method to derive dynamic equations for quantum fields far from equilibrium, surpassing traditional mean-field and Boltzmann approximations.

Contribution

It introduces a novel RG-based approach for non-equilibrium quantum field dynamics, deriving time evolution equations for the effective action and Green functions.

Findings

Equations are non-perturbative and go beyond mean-field approximations.

Derived dynamics agree with 1/N-expansion of the 2PI effective action.

The approach provides a new framework for quantum field evolution far from equilibrium.

Abstract

Dynamic equations for quantum fields far from equilibrium are derived by use of functional renormalisation group techniques. The obtained equations are non-perturbative and lead substantially beyond mean-field and quantum Boltzmann type approximations. The approach is based on a regularised version of the generating functional for correlation functions where times greater than a chosen cutoff time are suppressed. As a central result, a time evolution equation for the non-equilibrium effective action is derived, and the time-evolution of the Green functions is computed within a vertex expansion. It is shown that this agrees with the dynamics derived from the 1/N-expansion of the two-particle irreducible effective action.