Lawrence Berkeley Laboratory, Berkeley, California 94720.

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"Mean-Field Treatment of Non-Equilibrium Dynamics in Quantum Field Theory"**

The development of quantum field theory methods for the treatment of non-equilibrium problems has become an important focal point in theoretical physics. An especially challenging testing grounds for the theoretical approaches are provided by high-energy nuclear collisions.

The motivation for and context of the present work is first briefly highlighted. The physical problem underlying the work is the possibly occurrence of socalled Disoriented Chiral Condensates in high-energy collisions. The favorite theoretical tool has been the SU(2) linear model whose semi-classical implementation appears to be quantitatively useful. Moreover, its mean-field approximation seems to be good for scenarios of DCC relevance because the rapid cooling reduces the opportunity the quasi- particles to experience mutual scatterings. Finally, it appears possible to recast the field formulation of the model into a transport framework where individual test particles are propagated self-consistently in a medium characterized locally by an evolving chiral order parameter.

However, before relying quantitatively on such a calculational scheme, it is important take account of inherently quantal effects. Therefore, we have considered the quantum field evolution of a mean-field model with a time-dependent effective mass. The application of a method first conceived by Combescure yields expressions for the time evolution of the observables in terms of state-independent coefficients whose evolution can be (pre)determined on the basis of the given time-dependent mass. The resulting expressions show that the vacuum fluctuations are subject to the same amplification as the statistical fluctuations. It is finally demonstrated how the time-dependent enhancement coefficients for the particle number can be extracted from a purely classical treatment by exploiting the dependence of the resulting value of the observable on the phase of a given initial state. This result gives hope that it may become possible to incorporate the quantal enhancements into the classical treatment, which would then provide a quantitative calculational tool.