# An algebraic formulation of the locality principle in renormalisation

@article{Clavier2017AnAF, title={An algebraic formulation of the locality principle in renormalisation}, author={Pierre Clavier and Li Guo and Sylvie Paycha and Bin Zhang}, journal={European Journal of Mathematics}, year={2017}, volume={5}, pages={356-394} }

We study the mathematical structure underlying the concept of locality which lies at the heart of classical and quantum field theory, and develop a machinery used to preserve locality during the renormalisation procedure. Viewing renormalisation in the framework of Connes and Kreimer as the algebraic Birkhoff factorisation of characters on a Hopf algebra with values in a Rota–Baxter algebra, we build locality variants of these algebraic structures, leading to a locality variant of the algebraic…

## 14 Citations

### Renormalisation and locality: branched zeta values

- Mathematics
- 2018

Multivariate renormalisation techniques are implemented in order to build, study and then renormalise at the poles, branched zeta functions associated with trees. For this purpose, we first prove…

### Renormalisation via locality morphisms

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This is a survey on renormalisation in algebraic locality setup highlighting the role that locality morphisms can play for renormalisation purposes. After describing the general framework to build…

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The present exploratory paper deals with tensor products in the locality framework developed in previous work, a natural setting for an algebraic formulation of the locality principle in quantum ﬁeld…

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A bstract . Meromorphic germs in several variables with linear poles naturally arise in mathematics in various disguises. We investigate their rich structures under the prism of locality, including…

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- 2022

We prove a topological decomposition of the space of meromorphic germs at zero in several variables with prescribed linear poles as a sum of spaces of holomorphic and polar germs. Evaluating the…

### A conical approach to Laurent expansions for multivariate meromorphic germs with linear poles

- MathematicsPacific Journal of Mathematics
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We use convex polyhedral cones to study a large class of multivariate meromorphic germs, namely those with linear poles, which naturally arise in various contexts in mathematics and physics. We…

### Quivers and path semigroups characterized by locality conditions

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. The notion of locality semigroups was recently introduced with motivation from locality in convex geometry and quantum ﬁeld theory. We show that there is a natural correspondence between locality…

### Locality and causality in perturbative AQFT

- Mathematics
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In this paper we introduce a notion of a group with causality, which is a natural generalization of a locality group, introduced by P. Clavier, L. Guo, S. Paycha, and B. Zhang. We also propose a…

### From Orthocomplementations to Locality

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- 2021

After some background on lattices, the locality framework introduced in earlier work by the authors is extended to cover posets and lattices. We then extend the correspondence between Euclidean…

### Several locality semigroups, path semigroups and partial semigroups

- Mathematics
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Locality semigroups were proposed recently as one of the basic locality algebraic structures, which are studied in mathematics and physics. Path semigroups and partial semigroups were also developed…

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