An algebraic formulation of the locality principle in renormalisation

An algebraic formulation of the locality principle in renormalisation 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 paycha@math.uni-potsdam.de Pierre Clavier clavier@math.uni-potsdam.de Li Guo liguo@rutgers.edu Bin Zhang zhangbin@scu.edu.cn Institute of Mathematics, University of Potsdam, 14476 Potsdam, Germany Department of Mathematics, Jiangxi Normal University, Nanchang 330022, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png European Journal of Mathematics Springer Journals

An algebraic formulation of the locality principle in renormalisation

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Publisher
Springer International Publishing
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Algebraic Geometry
ISSN
2199-675X
eISSN
2199-6768
D.O.I.
10.1007/s40879-018-0255-8
Publisher site
See Article on Publisher Site

Abstract

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 paycha@math.uni-potsdam.de Pierre Clavier clavier@math.uni-potsdam.de Li Guo liguo@rutgers.edu Bin Zhang zhangbin@scu.edu.cn Institute of Mathematics, University of Potsdam, 14476 Potsdam, Germany Department of Mathematics, Jiangxi Normal University, Nanchang 330022,

Journal

European Journal of MathematicsSpringer Journals

Published: Jun 5, 2018

References

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