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

在标准模型中，核力用量子色动力学(QCD)来描述。K.Wilson[1]在1974年提出了在离散欧几里得时空上实现这一理论的开创性建议，而M.Creutz[2]在蒙特卡罗模拟方面的开创性工作在接下来的几十年里导致了第一原理的定量结果，再现了实验数据，从而为我们对这一理论的信任提供了基础。另一种基于朗之万方程的模拟方法也被采用了[3-5]。然而，一些与物理相关的问题是无法解决的--例如重离子碰撞和超稠密恒星，或者实时和非平衡情况下的动力学过程。在所有这些情况下，路径积分涉及复杂的动作，基于配置的正权重的数值方法不能应用。G.Parisi[6]和J.Klauder[7]很久以前提出的复朗之万(CL)方法原则上可以克服这些限制[5]，并被应用于晶格模型[8-10]。然而，该方法仍然有点可疑，因为在某些情况下，它会导致明显不正确的结果[11，12]，而且没有一系列的尝试来进一步开发它。直到最近，随着悬而未决的物理问题的出现，这种方法再次引起了人们的兴趣，此前J.Berges和I.-O.Stamatescu[13]以及G.Aart和I.-O.Stamatescu[14]提出了将其应用于动态实时过程的建议。这种方法的特点源于变量空间的复杂性，特别是正确收敛的形式证明依赖于附加条件[15]。到目前为止，在我们的分析中，我们遵循的是关于该方法的理论问题，以及它在现实模型中的应用。我们已经建立了确保正确收敛的量化标准，并开发了程序来果断地改善模拟的性质[16-19]。这使得应用于QCD相关模型[20-23]和完全QCD[24，25]成为可能。基于这些结果，除了进一步的方法论分析外，我们现在想要解决与突出的物理问题有关的精度问题。对于非零密度的QCD，目的是扩大可以获得可靠数据的参数范围，并在温度-化学势平面上绘制相图。特别是达到低温是研究超稠密物质行为等问题的一项重要任务。此外，我们现在想要解决我们在项目的第一部分中未能解决的问题，即实时动态过程。在这里，分析的目的也将是参数区域的扩展和应用到新的、现实的模型。引用参考包括在应用中的参考书目。

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.