14 citations · 58 across the 23 of their papers we have counts for
9 papers · 1 filter
TRAPs, Generalisations of MZVs, Locality and Resurgence for Quantum Field Theories
Pierre J. Clavier
This thesis presents some mathematical results related to quantum field theory. The first chapter is dedicated to TRAPs and how they could be used to rigorously define Feynman rule…
Borel-Ecalle resummation of a two-point function
Pierre J. Clavier
We provide an overview of the tools and techniques of resurgence theory used in the Borel-Ecalle resummation method, which we then apply to the massless Wess-Zumino model. Starting…
Locality and renormalisation: universal properties and integrals on trees
Pierre Clavier, Li Guo, Sylvie Paycha +1
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 i…
Renormalisation via locality morphisms
Pierre Clavier, Li Guo, Sylvie Paycha +1
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…
Renormalisation and locality: branched zeta values
Pierre Clavier, Li Guo, Sylvie Paycha +1
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,…
An algebraic formulation of the locality principle in renormalisation
Pierre Clavier, Li Guo, Sylvie Paycha +1
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 local…
Batalin-Vilkovisky formalism as a theory of integration for polyvectors
Pierre J. Clavier, Viet Dang Nguyen
The Batalin-Vilkovisky (BV) formalism is a powerful generalization of the BRST approach of gauge theories and allows to treat more general field theories. We will see how, starting…
Analytical and Geometric approches of non-perturbative Quantum Field Theories
Pierre J. Clavier
We present the Hopf algebra of renormalization and introduce the renormalization group equation in this framework. Some linear Schwinger--Dyson equations are studied, and exact sol…
A Schwinger--Dyson Equation in the Borel Plane: singularities of the solution
Marc P. Bellon, Pierre J. Clavier
We map the Schwinger--Dyson equation and the renormalization group equation for the massless Wess--Zumino model in the Borel plane, where the product of functions get mapped to a c…