Time evolution of linearized gauge field fluctuations on a real-time lattice

TL;DR

This paper develops a gauge-invariant lattice algorithm to simulate the evolution of classical gauge fields and small quantum fluctuations, crucial for understanding non-equilibrium dynamics in gauge theories like heavy-ion collisions.

Contribution

It introduces and tests a novel numerical method to accurately evolve gauge fields with linearized fluctuations while preserving gauge invariance and Gauss's law.

Findings

Algorithm maintains gauge invariance and Gauss's law on the lattice.

Enables detailed study of fluctuation effects in non-equilibrium gauge dynamics.

Provides a tool for more precise modeling of early-stage heavy-ion collisions.

Abstract

Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Due to instabilities, small quantum fluctuations on top of the classical background may significantly affect the dynamics of the system. In this paper we argue for the need for a numerical calculation of a system of classical gauge fields and small linearized fluctuations in a way that keeps the separation between the two manifest. We derive and test an explicit algorithm to solve these equations on the lattice, maintaining gauge invariance and Gauss's law.