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

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