Renormalisation via locality morphisms

TL;DR

This paper surveys the role of locality morphisms in renormalisation, presenting a general framework and illustrating applications in zeta functions and iterated integrals.

Contribution

It introduces a unified framework for renormalisation using locality algebra homomorphisms and demonstrates its application across multiple mathematical examples.

Findings

Framework for regularisation maps via locality morphisms

Application to poles of conical zeta functions

Application to branched zeta functions and iterated integrals

Abstract

This is a survey on renormalisation in the locality setup highlighting the role that locality morphisms can play for renormalisation purposes. Having set up a general framework to build regularisation maps, we illustrate renormalisation by locality algebra homomorphisms on three examples, the renormalisation at poles of conical zeta functions, branched zeta functions and iterated integrals stemming from Kreimer's toy model.