Some Remarks on Non-Planar Diagrams
High Energy Physics - Phenomenology
2013-12-20 v1
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.
Cite
@article{arxiv.1312.5603,
title = {Some Remarks on Non-Planar Diagrams},
author = {Krzysztof Bielas and Ievgen Dubovyk and Janusz Gluza and Tord Riemann},
journal= {arXiv preprint arXiv:1312.5603},
year = {2013}
}
Comments
Presented by K. Bielas at the International Conference of Theoretical Physics "Matter To The Deepest", Ustron 2013