Renormalization group and nonequilibrium action in stochastic field theory

TL;DR

This paper develops a renormalization group approach for nonequilibrium stochastic field theories, deriving flow equations from coarse graining of a closed-time-path action, and applies it to the KPZ equation.

Contribution

It introduces a novel renormalization group method based on coarse graining of the closed-time-path action for nonequilibrium systems, differing from traditional quantum field theory approaches.

Findings

Derived nontrivial RG flow from coarse graining of the closed-time-path action.

Showed the RG flow matches the dynamical RG from equations of motion.

Applied the method to derive the KPZ equation from the action.

Abstract

We investigate the renormalization group approach to nonequilibrium field theory. We show that it is possible to derive nontrivial renormalization group flow from iterative coarse graining of a closed-time-path action. This renormalization group is different from the usual in quantum field theory textbooks, in that it describes nontrivial noise and dissipation. We work out a specific example where the variation of the closed-time-path action leads to the so-called Kardar-Parisi-Zhang equation, and show that the renormalization group obtained by coarse graining this action, agrees with the dynamical renormalization group derived by directly coarse graining the equations of motion.