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 kinds 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.

Feynman diagrams via graphical calculus / Fiorenza, Domenico; Riccardo, Murri. - In: JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS. - ISSN 0218-2165. - 11:07(2002), pp. 1095-1131. [10.1142/s0218216502002165]

Feynman diagrams via graphical calculus

FIORENZA, DOMENICO;
2002

Abstract

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 kinds 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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11573/132729
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