Abstract

Speaker: Kurusch Ebrahimi-Fard, Bonn University, Physics Inst., Theory Dept.

Title: Quantum Field Theory and Rooted tree Hopf Algebras: an introduction to the recent work of Connes-Kreimer

Abstract:

Connes-Kreimer uncovered the mathematical structure underlying renormalization in perturbative QFT in terms of Hopf algebras of Feynman graphs. The process of renormalization -in short, subtraction of divergencies in a physical sound way- is captured by an algebraic Birkhoff decomposition of Feynman rules.

We will review this result in some detail with an emphasis on the factorization problem underlying the Birkhoff decomposition of Hopf algebra characters. At the end of the talk we briefly mention some current developments in this field.

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