Gluon Field Dynamics in Ultra-Relativistic Heavy-Ion Collisions: Time evolution on a Gauge Lattice in 3+1 Dimensions

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We describe the dynamics of gluons and quarks in a relativistic nuclear collision, within the framework of classical mean-field transport theory, by the coupled equations for the classical Yang-Mills field and a collection of colored point particles. The particles represent the valence quarks in the colliding nuclei. We explore the time evolution of the gauge field in a numerical simulation of the collision of two Lorentz-boosted ``nuclei'' on a long three-dimensional gauge lattice. We report first results on soft gluon scattering and coherent gluon radiation.