论文标题
生成和评估MSR字段理论的1Pi Feynman图
Generating and evaluating 1PI Feynman diagrams for an MSR field theory
论文作者
论文摘要
我们讨论了某些计算方法和分析技术，这些方法可用于自动化MSR字段理论重新归一化组分析中涉及的各个步骤。这些方法主要依赖于众所周知的feynarts和secdec。前者用于次要修改，用于生成Feynman图并获得相应的表达式，而后者用于Feynman积分的维度正则化和Epsilon扩展。我们首先讨论Feynarts所需的合适类和通用模型文件是如何创建内部文件Analytic.m中的次要修改，然后展示如何生成图表和表达式的。然后，我们讨论了从Feynman图获得的积分以进一步简化以标准标量Feynman积分形式渲染的过程，以便可以将软件包SECDEC用于尺寸正常化和Epsilon扩展它们。我们讨论了这些方法，因为它应用于特定理论，即NSAPS三矢量模型。但是，可以很容易地将它们推广到其他类似的MSR字段理论。
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.
