TY  - JOUR
A1  - Clavier, Pierre J.
T1  - Double shuffle relations for arborified zeta values
JF  - Journal of algebra
N2  - Arborified zeta values are defined as iterated series and integrals using the universal properties of rooted trees. This approach allows to study their convergence domain and to relate them to multiple zeta values. Generalisations to rooted trees of the stuffle and shuffle products are defined and studied. It is further shown that arborified zeta values are algebra morphisms for these new products on trees.
KW  - Rooted trees
KW  - Multiple zeta values
KW  - Shuffle products
KW  - Rota-Baxter
KW  - algebras
Y1  - 2020
U6  - https://doi.org/10.1016/j.jalgebra.2019.10.015
SN  - 0021-8693
SN  - 1090-266X
VL  - 543
SP  - 111
EP  - 155
PB  - Elsevier
CY  - San Diego
ER  - 
TY  - JOUR
A1  - Clavier, Pierre J.
T1  - Borel-Écalle resummation of a two-point function
JF  - Annales Henri Poincaré : a journal of theoretical and mathematical physics / ed. jointly by the Institut Henri Poincaré and by the Swiss Physical Society
N2  - 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 from already known results on the anomalous dimension of the Wess-Zumino model, we solve its renormalisation group equation for the two-point function in a space of formal series. We show that this solution is 1-Gevrey and that its Borel transform is resurgent. The Schwinger-Dyson equation of the model is then used to prove an asymptotic exponential bound for the Borel transformed two-point function on a star-shaped domain of a suitable ramified complex plane. This proves that the two-point function of the Wess-Zumino model is Borel-ecalle summable.
Y1  - 2021
U6  - https://doi.org/10.1007/s00023-021-01057-w
SN  - 1424-0637
SN  - 1424-0661
VL  - 22
IS  - 6
SP  - 2103
EP  - 2136
PB  - Springer
CY  - Cham
ER  - 
TY  - JOUR
A1  - Clavier, Pierre J.
A1  - Guo, Li
A1  - Paycha, Sylvie
A1  - Zhang, Bin
T1  - An algebraic formulation of the locality principle in renormalisation
JF  - European Journal of Mathematics
N2  - 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 Birkhoff factorisation. This provides an algebraic formulation of the conservation of locality while renormalising. As an application in the context of the Euler-Maclaurin formula on lattice cones, we renormalise the exponential generating function which sums over the lattice points in a lattice cone. As a consequence, for a suitable multivariate regularisation, renormalisation from the algebraic Birkhoff factorisation amounts to composition by a projection onto holomorphic multivariate germs.
KW  - Locality
KW  - Renormalisation
KW  - Algebraic Birkhoff factorisation
KW  - Partial algebra
KW  - Hopf algebra
KW  - Rota-Baxter algebra
KW  - Multivariate meromorphic functions
KW  - Lattice cones
Y1  - 2019
U6  - https://doi.org/10.1007/s40879-018-0255-8
SN  - 2199-675X
SN  - 2199-6768
VL  - 5
IS  - 2
SP  - 356
EP  - 394
PB  - Springer
CY  - Cham
ER  - 
TY  - CHAP
A1  - Clavier, Pierre J.
A1  - Guo, Li
A1  - Paycha, Sylvie
A1  - Zhang, Bin
T1  - Renormalisation and locality
BT  - branched zeta values
T2  - Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA)
Volume 2
Y1  - 2020
SN  - 978-3-03719-205-4 print
SN  - 978-3-03719-705-9 online
U6  - https://doi.org/10.4171/205
SP  - 85
EP  - 132
PB  - European Mathematical Society Publishing House
CY  - Zürich
ER  -