Loops on surfaces, Feynman diagrams, and trees - INSPIRE

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Loops on surfaces, Feynman diagrams, and trees

Vladimir Turaev
(
- IRMA, Strasbourg
)

Mar, 2004

9 pages

Published in:

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

e-Print:

hep-th/0403266 [hep-th]

DOI:

10.1016/j.geomphys.2004.07.010

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Abstract:

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.

rooted trees
pre-Lie algebras
Connes-Kreimer coproduct
algebra: Lie
Feynman graph: higher-order

References(4)

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- Annals Math. 78 267

- Adv.Math. 54 200

- Trans.Moscow Math.Soc. 12 340

- Chin.Ann.Math. 2 117