An algebraic formulation of the locality principle in renormalisation

DOI10.1007/s40879-018-0255-8zbMath1467.81074arXiv1711.00884OpenAlexW2963255860MaRDI QIDQ1999230

Bin Zhang, Li Guo, Sylvie Paycha, Pierre J. Clavier

Publication date: 26 June 2019

Published in: European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.00884

zbMATH Keywords

Hopf algebralocalityrenormalisationRota-Baxter algebrapartial algebramultivariate meromorphic functionslattice conesalgebraic Birkhoff factorisation

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Perturbative methods of renormalization applied to problems in quantum field theory (81T15) Meromorphic functions of several complex variables (32A20) Partial algebras (08A55) Hopf algebras, quantum groups and related topics (16T99)

Related Items

Renormalization of Feynman amplitudes on manifolds by spectral zeta regularization and blow-ups, Locality and renormalization: Universal properties and integrals on trees, Quivers and path semigroups characterized by locality conditions, Mathematical reflections on locality, Locality Galois groups of meromorphic germs in several variables, From orthocomplementations to locality, Locality and causality in perturbative algebraic quantum field theory, Renormalisation and locality: branched zeta values, A conical approach to Laurent expansions for multivariate meromorphic germs with linear poles

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A note on the Wehrheim-Woodward category
• Renormalization and quantum field theory
• Algebraic Birkhoff factorization and the Euler-Maclaurin formula on cones
• Perturbative algebraic quantum field theory and the renormalization groups
• Proof of the Bogoliubov-Parasiuk theorem on renormalization
• Über die Multiplikation der Kausalfunktionen in der Quantentheorie der Felder
• Renormalisation and locality: branched zeta values
• A conical approach to Laurent expansions for multivariate meromorphic germs with linear poles
• Renormalization of multiple zeta values
• On the locality ideal in the algebra of test functions for quantum fields
• The Hopf algebras of decorated rooted trees. I
• Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem
• Selective categories and linear canonical relations
• Renormalization of Feynman amplitudes on manifolds by spectral zeta regularization and blow-ups
• Exponential renormalisation. II. Bogoliubov's R-operation and momentum subtraction schemes
• A smooth introduction to the wavefront set
• Nested Sums of Symbols and Renormalized Multiple Zeta Values
• Properties of field functionals and characterization of local functionals
• The Hopf Algebra of ($q$-)Multiple Polylogarithms with Non-positive Arguments: Table 1.
• Renormalization in Quantum Field Theory (after R. Borcherds)
• On structure of the algebra of field operators