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Feynman Diagrams via Graphical Calculus

Domenico Fiorenza·Riccardo Murri
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Abstract

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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Domenico Fiorenza, Riccardo Murri. 2001-08-02. Feynman Diagrams via Graphical Calculus. https://arxiv.org/abs/math/0106001

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