Flowing with the Temporal Renormalisation Group

TL;DR

This paper applies the temporal functional renormalisation group to study the far-from-equilibrium dynamics of 1+1 dimensional $^3$-theory, deriving novel equations and analyzing self-similar behavior and conservation laws.

Contribution

It introduces a causal, one-loop exact framework for computing fully dressed correlation functions in non-equilibrium quantum field theory.

Findings

Numerical computation of the dynamical propagator shows self-similarity far from equilibrium.

Scaling exponents are discussed for the observed self-similar behavior.

Energy and particle number are numerically conserved in the simulations.

Abstract

We discuss the far-from-equilibrium evolution of $\phi^3$-theory in $1+1$ dimensions with the temporal functional renormalisation group \cite{Gasenzer:2007za, Gasenzer:2010rq}. In particular, we show that this manifestly causal approach leads to novel one-loop exact equations for fully dressed correlation functions. Within this setup, we numerically compute the dynamical propagator. Its behaviour suggests self-similarity far from equilibrium in a restricted momentum regime. We discuss the scaling exponents for our solution, as well as the numerical satisfaction of energy and particle number conservation. We also derive a simple exact representation of the expectation value of the energy-momentum tensor solely in terms of the propagator.