Loops on surfaces, Feynman diagrams, and trees

Details Loops on surfaces, Feynman diagrams, and trees Loops on surfaces, Feynman diagrams, and trees

2004-03-26

arxiv.org/abs/hep-th/0403266v6

J.Geom.Phys. 53 (2005) 461-482

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, no figures. Added sections on Hopf algebras, Wilson loops on surfaces and knot diagrams

Scientific paper

10.1016/j.geomphys.2004.07.010

We relate the author's Lie cobracket in the module additively generated by
loops on a surface with the Connes-Kreimer Lie bracket in the module additively
generated by trees. To this end we introduce a pre-Lie coalgebra and a
(commutative) Hopf algebra of pointed loops on a surface. In the last version I
added sections on Wilson loops and knot diagrams.

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