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arXiv · 1312.5603

Some Remarks on Non-Planar Diagrams

Krzysztof Bielas·Ievgen Dubovyk·Janusz Gluza·Tord Riemann
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Abstract

Two criteria for planarity of a Feynman diagram upon its propagators (momentum flows) are presented. Instructive Mathematica programs that solve the problem and examples are provided. A simple geometric argument is used to show that while one can planarize non-planar graphs by embedding them on higher-genus surfaces (in the example it is a torus), there is still a problem with defining appropriate dual variables since the corresponding faces of the graph are absorbed by torus generators.

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Krzysztof Bielas, Ievgen Dubovyk, Janusz Gluza, Tord Riemann. 2013-12-19. Some Remarks on Non-Planar Diagrams. https://doi.org/10.5506/aphyspolb.44.2249

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