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Real-Time Evolution of Soft Gluon Field Dynamics in Ultra-Relativistic Heavy-Ion Collisions

The dynamics of gluons and quarks in a relativistic nuclear collision are described, within the framework of a classical mean-field transport theory, by the coupled equations for the Yang-Mills field and a collection of colored point particles. The particles are used to represent color source effects of the valence quarks in the colliding nuclei. The possibilities of this approach are studied to describe the real time evolution of small $x$ modes in the classical effective theory in a non-perturbative coherent manner. The time evolution of the color fields is explored in a numerical simulation of the collision of two Lorentz-boosted clouds of color charged particles on a long three-dimensional gauge lattice. We report results on soft gluon scattering and coherent gluon radiation obtained in SU(2) gauge symmetry.