# Renormalization and periods in perturbative Algebraic Quantum Field Theory

March 09, 2016

In this paper I give an overview of mathematical structures appearing in
perturbative algebraic quantum field theory (pAQFT) and I show how these relate
to certain periods. pAQFT is a mathematically rigorous framework that allows to
build models of physically relevant quantum field theories on a large class of
Lorentzian manifolds. The basic objects in this framework are functionals on
the space of field configurations and renormalization method used is the
Epstein-Glaser (EG) renormalization. The main idea in the EG approach is to
reformulate the renormalization problem, using functional analytic tools, as a
problem of extending almost homogeneously scaling distributions that are well
defined outside some partial diagonals in $\mathbb{R}^n$. Such an extension is
not unique, but it gives rise to a unique "residue", understood as an
obstruction for the extended distribution to scale almost homogeneously.
Physically, such scaling violations are interpreted as contributions to the
$\beta$ function.

Keywords:

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