QCD and other models at finite density, Stochastic Quantisation, Non-equilibriumphenomena in Quantum Field Theories.

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In the Standard Modell the nuclear forces are described by Quantum Chromodynamics (QCD). The seminal proposal of K. Wilson [1] from 1974 to realise this theory on a discretized euclidean space-time, and the pioneering work of M. Creutz [2] on Monte Carlo simulations led in the following decades to quantitative results from first principles reproducing the experimental data and thus providing the basis for our trust in this theory. Another simulation method, based on the Langevin equation, has also been followed [3-5].Some physically relevant questions were however not accessible - such as heavy ion collisions and super-dense stars, or dynamical processes in real time and non-equilibrium situations. In all these cases the path integral involves a complex action and numerical methods based on a positive weighting of the configurations could not be applied. The complex Langevin (CL) method, proposed long ago by G. Parisi [6] and J. Klauder [7] allows in principle to overcome these limitations [5] and was applied to lattice models [8-10]. However the method remained slightly suspect, since in some cases it would lead to clearly incorrect results [11,12] and there was no serios attempt to further develop it. Only recently, with the rising of outstanding physical questions this method found again interest, following the proposals to apply it to dynamical real time processes by J. Berges and I.-O. Stamatescu [13] as well as to QCD at non-zero chemical potential by G. Aarts and I.-O. Stamatescu [14].The peculiarities of this method follow from the complexification of the variable space, in particular the formal proof for correct convergence depends on additional conditions [15]. In our analysis until now we have followed theoretical questions concerning the method, and its application to realistic models. We have established quantitative criteria to ensure correct convergence and developed procedures to improve the properties of the simulations decisively [16-19]. This made the application to QCD-related models [20-23] and to full QCD [24,25] possibble.Based on these results we now want to attack precision questions concerning outstanding physical problems, besides further methodological analyses. Concerning QCD at non-zero density the aim is to expand the region of parameters in which reliable data can be obtained and to draw the phase diagram in the temperature-chemical potential plane. Especially reaching low temperatures is an important task for approaching such questions as the behaviour of super-dense matter.Moreover we want to address now questions which we could not pursue in the first part of the project, namely dynamical processes in real time. Here also the aims of the analysis will be the extension of the parameter region and of the application to new, realistic models.The citations refer to the Bibliography included in the application.