Plasmon mass scale and quantum fluctuations of classical fields on a real time lattice

TL;DR

This paper investigates the plasmon mass scale and quantum fluctuations in classical gauge fields on a lattice, crucial for modeling early-stage heavy-ion collisions and understanding non-equilibrium gauge theory dynamics.

Contribution

It introduces a numerical method to accurately separate classical gauge fields from quantum fluctuations and tests its effectiveness in lattice simulations.

Findings

Determined the plasmon mass using three different methods.

Validated the linearization of quantum fluctuations in classical gauge fields.

Confirmed Gauss's law conservation in the implemented algorithm.

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. Above the Debye scale the classical Yang-Mills (CYM) theory can be matched smoothly to kinetic theory. First we study the limits of the quasiparticle picture of the CYM fields by determining the plasmon mass of the system using 3 different methods. Then we argue that one needs a numerical calculation of a system of classical gauge fields and small linearized fluctuations which correspond to quantum fluctuations, in a way that keeps the separation between the two manifest. We demonstrate and test an implementation of an algorithm with the linearized fluctuations showing that the linearization indeed works and the Gauss's law is conserved.