MSR场论的1PI费曼图的生成和计算
Generating and evaluating 1PI Feynman diagrams for an MSR field theory
摘要：
我们讨论了某些计算方法和分析技术，可用于自动化的重整化群分析的MSR场论的各个步骤。这些方法主要依赖于众所周知的软件包FeynArts和SecDec。前者用于生成Feynman图并获得相应的表达式，后者用于Feynman积分的维数正则化和展开。我们首先讨论如何创建FeynArts所需的合适的类和通用模型文件，介绍在内部文件Analytic. m中所做的微小修改，然后展示如何生成图表和表达式。然后，我们讨论的程序，在进一步简化的积分从费曼图，使他们在标准的标量费曼图积分的形式，使软件包SecDec可以用来尺寸正则化和扩展。我们讨论这些方法，因为它是适用于一个特定的理论，即NSAPS三矢量模型。然而，它们可以很容易地推广到其他类似的MSR场论。
英文摘要：
We discuss certain computational methods and analytical techniques that can be used to automatize the various steps involved in the renormalization group analysis of an MSR field theory. The methods rely mainly on the well known packages FeynArts and SecDec. The former is used with minor modifications for generating the Feynman diagrams and obtaining the corresponding expressions, and the latter for dimensional regularization and epsilon expansion of the Feynman integrals. We first discuss how suitable classes and generic model files required by FeynArts are created, present the minor modifications made in the internal file Analytic.m, and then show how the diagrams and the expressions are generated. We then discuss the procedure followed in further simplifying the integrals obtained from the Feynman diagrams to render them in the form of standard scalar Feynman integrals so that the package SecDec can be used to dimensional regularize and epsilon expand them. We discuss these methods as it is applied to a particular theory, namely, the NSAPS three-vector model. However, they can be easily generalized to be applied to other similar MSR field theories.
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