  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.
