@article{ClavierGuoPaychaetal.2019,
  author    = {Clavier, Pierre J. and Guo, Li and Paycha, Sylvie and Zhang, Bin},
  title     = {An algebraic formulation of the locality principle in renormalisation},
  series = {European Journal of Mathematics},
  volume    = {5},
  journal   = {European Journal of Mathematics},
  number    = {2},
  publisher = {Springer},
  address   = {Cham},
  issn      = {2199-675X},
  doi       = {10.1007/s40879-018-0255-8},
  pages     = {356 -- 394},
  year      = {2019},
  abstract  = {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.},
  language  = {en}
}