Classical real-time lattice simulations play animportant role in understanding non-equilibrium phenomenain gauge theories and are used in particular to model theprethermal evolution of heavy-ion collisions. Due to instabilities,small quantum fluctuations on top of the classical backgroundmay significantly affect the dynamics of the system.In this paper we argue for the need for a numerical calculationof a system of classical gauge fields and small linearized fluctuationsin a way that keeps the separation between the twomanifest. We derive and test an explicit algorithm to solvethese equations on the lattice, maintaining gauge invarianceand Gauss’ law.
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