Classical gluon radiation in ultrarelativistic nucleus-nucleus collisions

The classical Yang-Mills equations are solved perturbatively in covariant gauge for a collision of two ultrarelativistic nuclei. The nuclei are taken as ensembles of classical color charges on eikonal trajectories. The classical gluon field is computed in coordinate space up to cubic order in the coupling constant $g$. We construct the Feynman diagrams corresponding to this field and show the equivalence of the classical and diagrammatic approaches. An argument is given which demonstrates that at higher orders in $g$ the classical description of the process breaks down. As an application, we calculate the energy, number, and multiplicity distributions of produced soft gluons and reproduce earlier results by Gunion and Bertsch and by Kovner, McLerran, and Weigert.