费曼图的图形演算
Feynman Diagrams via Graphical Calculus
摘要：
本文介绍了费曼图语言。我们使用Reshetikhin-Turaev图形演算来定义Feynman图，并证明了高斯积分的渐近展开可以写成一个适当的图形族的总和。我们讨论了不同类型的相互作用如何产生不同的图族。特别是，我们展示了如何对称和循环的相互作用导致“普通”和“丝带”的图形分别。作为一个例子，对二维量子引力的t Hooft-Kontsevich模型作了较详细的讨论。
英文摘要：
This paper is an introduction to the language of Feynman Diagrams. We use Reshetikhin-Turaev graphical calculus to define Feynman diagrams and prove that asymptotic expansions of Gaussian integrals can be written as a sum over a suitable family of graphs. We discuss how different kind of interactions give rise to different families of graphs. In particular, we show how symmetric and cyclic interactions lead to ``ordinary'' and ``ribbon'' graphs respectively. As an example, the 't Hooft-Kontsevich model for 2D quantum gravity is treated in some detail.
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