Nonequilibrium dynamics: a renormalized computation scheme

TL;DR

This paper introduces a renormalized computational scheme for non-equilibrium dynamics in classical fields coupled to quantum fluctuations, enabling flexible regularization and renormalization methods, demonstrated on a scalar phi^4 theory.

Contribution

It develops a regularized and renormalized one-loop relaxation equation framework with separated divergent and finite parts, allowing flexible regularization schemes like dimensional regularization.

Findings

The method effectively computes non-equilibrium evolution in scalar phi^4 theory.

Results align with previous studies, validating the approach.

Energy-momentum tensor renormalization monitors numerical reliability.

Abstract

We present a regularized and renormalized version of the one-loop nonlinear relaxation equations that determine the non-equilibrium time evolution of a classical (constant) field coupled to its quantum fluctuations. We obtain a computational method in which the evaluation of divergent fluctuation integrals and the evaluation of the exact finite parts are cleanly separated so as to allow for a wide freedom in the choice of regularization and renormalization schemes. We use dimensional regularization here. Within the same formalism we analyze also the regularization and renormalization of the energy-momentum tensor. The energy density serves to monitor the reliability of our numerical computation. The method is applied to the simple case of a scalar phi^4 theory; the results are similar to the ones found previously by other groups.