Feynman Diagrams via Graphical Calculus

Details Feynman Diagrams via Graphical Calculus Feynman Diagrams via Graphical Calculus

2001-05-31

arxiv.org/abs/math/0106001v2

J.Knot Theor.Ramifications 11 (2002) 1095-1132

Mathematics

Quantum Algebra

30 pages, AMS-LaTeX, 19 EPS figures + several in-text XY-Pic, PostScript \specials, corrected attributions, 'PROP's instead of

Scientific paper

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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