Communications in Number Theory and Physics

Volume 9 (2015)

Number 3

Wonderful compactifications in quantum field theory

Pages: 477 – 547



Marko Berghoff (Institut für Mathematik, Humboldt-Universität, Berlin, Germany)


In [3] it was shown how so-called wonderful compactifications can be used for renormalization in the position space formulation of quantum field theory. This article aims to continue this idea, using 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 [16] where wonderful models were studied from a purely combinatorial viewpoint. The main motivation behind this approach is the fact that both, perturbative 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.

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