Yang-Mills theories are an important building block of the standard model and in particular of quantum chromodynamics. Its correlation functions describe the behavior of its elementary particles, the gauge bosons. In quantum chromodynamics, the correlation functions of the gluons are basic ingredients for calculations of hadrons from bound state equations or properties of its phase diagram with functional methods. Correlation functions of gluons are defined only in a gauge fixed setting. The focus of many studies is the Landau gauge which has some features that alleviate calculations. I discuss recent results of correlation functions in this gauge obtained from their equations of motions. Besides the four-dimensional case also two and three dimensions are treated, since the effects of truncations, viz., the procedure to render the infinitely large system of equations finite, can be studied more directly in these cases. In four dimensions, the anomalous running of dressing functions plays a special role and it is explained how resummation is realized in the case of Dyson-Schwinger equations. Beyond the Landau gauge other gauges can provide additional insights or can alleviate the development of new methods. Some aspects or ideas are more easily accessible in alternative gauges and the results presented here for linear covariant gauges, the Coulomb gauge and the maximally Abelian gauge help to refine our understanding of Yang-Mills theories.

中文翻译：

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Yang-Mills 理论的非微扰性质

Yang-Mills 理论是标准模型，尤其是量子色动力学的重要组成部分。它的相关函数描述了它的基本粒子规范玻色子的行为。在量子色动力学中，胶子的相关函数是从束缚态方程或其相图的性质用泛函方法计算强子的基本成分。胶子的相关函数仅在规范固定设置中定义。许多研究的重点是朗道规，它具有一些减轻计算的功能。我讨论了从运动方程中获得的这个规范中相关函数的最新结果。除了四维情况外，还处理二维和三维情况，因为截断的影响，即，在这些情况下，可以更直接地研究将无限大的方程组变为有限的过程。在四个维度上，修整函数的异常运行起到了特殊的作用，并在Dyson-Schwinger方程的情况下解释了如何实现求和。除了朗道量规，其他量规可以提供额外的见解或可以减轻新方法的开发。某些方面或想法在替代规范中更容易获得，这里介绍的线性协变规范、库仑规范和最大阿贝尔规范的结果有助于完善我们对杨-米尔斯理论的理解。修整函数的异常运行起着特殊的作用，并解释了如何在戴森-施温格方程的情况下实现求和。除了朗道量规之外，其他量规可以提供额外的见解或可以减轻新方法的开发。某些方面或想法在替代规范中更容易获得，这里介绍的线性协变规范、库仑规范和最大阿贝尔规范的结果有助于完善我们对杨-米尔斯理论的理解。修整函数的异常运行起着特殊的作用，并解释了如何在戴森-施温格方程的情况下实现求和。除了朗道量规，其他量规可以提供额外的见解或可以减轻新方法的开发。某些方面或想法在替代规范中更容易获得，这里介绍的线性协变规范、库仑规范和最大阿贝尔规范的结果有助于完善我们对杨-米尔斯理论的理解。