Wonderful compactifications in quantum field theory

Author: 

Berghoff, M

Publication Date: 

1 January 2015

Journal: 

Communications in Number Theory and Physics

Last Updated: 

2021-04-10T03:14:32.5+01:00

Issue: 

3

Volume: 

9

DOI: 

10.4310/cntp.2015.v9.n3.a2

page: 

477-547

abstract: 

This article reviews the use of DeConcini-Procesi wonderful models in
renormalization of ultraviolet divergences in position space as introduced by
Bergbauer, Brunetti and Kreimer. In contrast to the exposition there we employ
a slightly different approach; instead of the subspaces in the arrangement of
divergent loci, we use the poset of divergent subgraphs as the main tool to
describe the whole renormalization process. This is based on an article by
Feichtner, where wonderful models were studied from a purely combinatorial
viewpoint. The main motivation for this approach is the fact that both,
renormalization and the model construction, are governed by the combinatorics
of this poset. Not only simplifies this the exposition considerably, but also
allows to study the renormalization operators in more detail. Moreover, we
explore the renormalization group in this setting by studying how the
renormalized distributions behave under a change of renormalization points.

Symplectic id: 

1141027

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article