Refine
Has Fulltext
- no (1) (remove)
Year of publication
- 2019 (1) (remove)
Document Type
- Article (1) (remove)
Language
- English (1)
Is part of the Bibliography
- yes (1)
Keywords
- Algebraic Birkhoff factorisation (1)
- Hopf algebra (1)
- Lattice cones (1)
- Locality (1)
- Multivariate meromorphic functions (1)
- Partial algebra (1)
- Renormalisation (1)
- Rota-Baxter algebra (1)
Institute
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.