Loops on surfaces, Feynman diagrams, and trees

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.

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

References in corpus (1)

• Virtual strings and their cobordisms

Cited by in corpus (5)

• Combinatorial Hopf algebras in quantum field theory I
• Hopf algebras in renormalization theory: Locality and Dyson-Schwinger equations from Hochschild cohomology
• Hopf algebra approach to Feynman diagram calculations
• Graph complexes and Feynman rules
• The necklace Lie coalgebra and renormalization algebras