Gustav Karreskog: Hopf algebras and Feynman graphs

Our main purpose in this project is to study several Hopf algebras of Feynman graphs, and do some calculations of the values of an antipode on concrete graphs. These Feynman graph Hopf algebras originated in the quantum field theory, more precisely in a relatively new approach to the renormalization of diverging Feynman integrals. In that approach to renormalization the antipode map plays a key role. We give a comprehensive introduction into the theory of graded Hopf algebras. We describe in detail all the main definitions and theorems necessary to understand Hopf algebras of Feynman graphs, and consider many concrete graphs.