# 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.

open access link

@inproceedings{Rejzner:2016wiy,
author = "Rejzner, Kasia",
title = "{Renormalization and periods in perturbative Algebraic
Quantum Field Theory}",
url = "http://inspirehep.net/record/1426845/files/arXiv:1603.02748.pdf",
year = "2016",
eprint = "1603.02748",
archivePrefix = "arXiv",
primaryClass = "math-ph",
SLACcitation = "%%CITATION = ARXIV:1603.02748;%%"
}

Keywords:

*none*