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Manuscript Title: Collision of SU(2) gauge fields in 3 + 1 dimensions.
Authors: W. Poschl, B. Muller
Program title: ym3dsu2.cc
Catalogue identifier: ADLN_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 125(2000)282
Programming language: C++.
Computer: any Unix workstation, Linux PC, Cray T3E.
Operating system: UNIX.
Keywords: Particle physics, Elementary, Qcd, Gauge lattice theory, Yang-mills theory, Gluon fields, Su(2) gauge symmetry, Yang-mills equation, Numerical simulation, Time-evolution, Wave packets, Ultra-relativistic, Heavy-ion collision.
Classification: 11.5.

Nature of problem:
Coherence effects are important in the description of the formation and evolution of the quark gluon plasma in ultra-relativistic heavy-ion collisions. In particular the description of the initial state of the two colliding nuclei requires the coherent evolution of colour fields generated by random sources. In order to develop an appropriate transport model for the early stage of high energetic nuclear collisions it is therefore necessary to study first pure Yang-Mills field dynamics as a coherent mean-field model for the gluon fields.

Solution method:
Gluon dynamics at small x can be viewed as coherent Yang-Mills dynamics with fast random colour sources. Therefore, it is useful to study classical Yang-Mills dynamics in three dimensions. The computer program presented here, allows a demonstration of the simple cases.
The soft gluon fields of two colliding nuclei are modelled as Gaussian wave packets in the framework of Yang-Mills theory. In this simple approach valence quarks and sea quarks are omitted. The structure of the nuclei is neglected or smeared out by initially uniform field distributions.
The dynamics of colour degrees of freedom is considered within the framework of a SU(2) gauge symmetry. Soft gluon scattering and time-delayed gluon radiation are studied with this simple mean-field approach by an analysis of the time evolution of energy currents and energy distributions in various dimensions and projections as well as their Fourier spectra. The time evolution of the fields is described by the Yang-Mills equations and carried out on a gauge lattice within the Hamiltonian formulation of Kogut and Susskind.

In the present version of the code we only consider Yang-Mills fields and their time-evolution in the SU(2) gauge symmetry. The extension towards SU(N) gauge symmetry can be carried out in a straight forward manner. Uniformly colour polarized wave packets of Gaussian shape are used to describe the soft glue fields of two colliding nuclei.