Fluctuations of the initial color fields in high-energy heavy-ion collisions

In the color glass condensate approach to the description of high-energy heavy-ion collisions, one needs to superimpose small random Gaussian distributed fluctuations to the classical background field in order to resum the leading secular terms that result from the Weibel instability, which would otherwise lead to pathological results beyond leading order. In practical numerical simulations, one needs to know this spectrum of fluctuations at a proper time Qₒ^-1 shortly after the collision, in the Fock-Schwinger gauge A^=0. In this paper, we derive these fluctuations from first principles by solving the Yang-Mills equations linearized around the classical background, with plane wave initial conditions in the remote past. We perform the intermediate steps in light-cone gauge, and we convert the results to the Fock-Schwinger gauge at the end. We obtain simple and explicit formulas for the fluctuation modes.