Locality and renormalisation: universal properties and integrals on trees
Mathematical Physics
2020-02-11 v2 Commutative Algebra
Complex Variables
math.MP
Abstract
The purpose of this paper is to build an algebraic framework suited to regularise branched structures emanating from rooted forests and which encodes the locality principle. This is achieved by means of the universal properties in the locality framework of properly decorated rooted forests. These universal properties are then applied to derive the multivariate regularisation of integrals indexed by rooted forests. We study their renormalisation, along the lines of Kreimer's toy model for Feynman integrals.
Cite
@article{arxiv.1811.01215,
title = {Locality and renormalisation: universal properties and integrals on trees},
author = {Pierre Clavier and Li Guo and Sylvie Paycha and Bin Zhang},
journal= {arXiv preprint arXiv:1811.01215},
year = {2020}
}
Comments
25 pages