Flowing with the temporal renormalization group
Lukas Corell, Anton K. Cyrol, Markus Heller, Jan M. Pawlowski
Abstract
We discuss the far-from-equilibrium evolution of ${\ensuremath{\phi}}^{3}$ theory in $1+1$ dimensions with the temporal functional renormalization group. 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 behavior 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.