Collision of SU(2) gauge fields in 3+1 dimensions

Abstract

The Yang–Mills equations provide a classical mean field description of the non-Abelian soft glue field dynamics in heavy ion collisions at high energies. A C++ code for the numerical solution on a three-dimensional gauge lattice is presented. Non-perturbative time-dependent solutions in position space are calculated in the weak coupling regime of a gauge lattice within the Hamiltonian approach of Kogut and Susskind. Applications are demonstrated by simulations of the Yang–Mills field dynamics in collisions of initially uniformly color polarized Gaussian wave packets. The collisions are evolved in time. The time dependent energy densities, energy flows and energy currents in longitudinal and transverse directions with respect to the collision axis are presented. Simulations of this type have recently revealed an interesting solution which exhibits a time-delayed sudden increase of the transverse energy currents in the “non-Abelian case” at short times after the collision.