|
Abstract:
The renormalization procedure in perturbative quantum
field theory seeks to extract finite quantities from divergent expansions of
feynman Graphs. For a long time a seemingly "ad hoc" algorithm, it was put
on solid algebraic footing in the work of Kreimer and Connes-Kreimer, by
introducing a Hopf algebra structure on Feynman graphs, and relating the
renormalized quantities to the twisted antipode in this Hopf algebra.
I will given an introduction to these ideas, and discuss recent joint work
with Kobi Kremnizer, showing how the above Hopf algebra structure can be
seen to arise from the structure of a category on Feynman graphs, closely
resembling that of a finitary abelian category. From this perspective, the
Connes-Kreimer Hopf algebra is dual to the Ringel-Hall algebra of the
category.
|