Title: The combinatorics of parametric Feynman integrals
|Affiliation:||University of Waterloo|
Feynman integrals are used in perturbative quantum field theory to compute the probabilities of processes involving elementary particles. They can be represented as Feynman graphs and exhibit a rich combinatorial structure. The parametric representation of Feynman integrals is particularly suitable to be studied from a combinatorial perspective since it contains well known objects like the Kirchhoff polynomial.
I will give a general introduction to parametric Feynman integrals and discuss some specific topics like linear reducibility and the $c_2$-invariant that are combinatorially interesting. Following that I will introduce the corolla polynomial and explain how its associated differential operator can be used to generalize parametric Feynman integrals from the relatively simple “scalar” case to any gauge theory. These generalized integrals quickly become exceedingly complicated which makes even small examples difficult to integrate in practice. In the last part of the talk I will report on recent efforts to find combinatorial structures in the integrands that significantly simplify them in the particular case of quantum electrodynamics.
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