European Journal of Mathematics https://doi.org/10.1007/s40879-018-0255-8 RESEARCH ARTICLE An algebraic formulation of the locality principle in renormalisation 1 2,3 4,5 Pierre Clavier · Li Guo · Sylvie Paycha · Bin Zhang Received: 25 November 2017 / Revised: 20 April 2018 / Accepted: 26 April 2018 © Springer International Publishing AG, part of Springer Nature 2018 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 renormalisa- tion 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 Sylvie Paycha, on leave from Université Clermont-Auvergne. The authors acknowledge supports from the Natural Science Foundation of China (Grant Nos. 11521061 and 11771190) and the German Research Foundation (DFG Grant PA 1686/6-1). They are grateful to the hospitalities of Sichuan University and University of Potsdam where parts of the work were completed. B Sylvie Paycha email@example.com Pierre Clavier firstname.lastname@example.org Li Guo email@example.com Bin Zhang firstname.lastname@example.org Institute of Mathematics, University of Potsdam, 14476 Potsdam, Germany Department of Mathematics, Jiangxi Normal University, Nanchang 330022,
European Journal of Mathematics – Springer Journals
Published: Jun 5, 2018
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