Graphs in perturbation theory: Algebraic structure and asymptotics

Understand

This thesis provides an extension of the work of Dirk Kreimer and Alain Connes on the Hopf algebra structure of Feynman graphs and renormalization to general graphs.

• Additionally, an algebraic structure of the asymptotics of formal power series with factorial growth, which is compatible with the Hopf algebraic structure, is introduced.
• The Hopf algebraic structure on graphs permits the explicit enumeration of graphs with constraints for the allowed subgraphs.
• In the case of Feynman diagrams a lattice structure, which will be introduced, exposes additional unique properties for physical quantum field theories.