Lessons from quantum field theory: Hopf algebras and spacetime geometries

DOI10.1023/A:1007523409317zbMath0965.81046arXivhep-th/9904044OpenAlexW2996458171MaRDI QIDQ1306725

Alain Connes, Dirk Kreimer

Publication date: 20 December 1999

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9904044

zbMATH Keywords

quantum field theoryHopf algebra of rooted treesRunge-Kutta methodsfoliationsmultiple zeta valuesiterated integralsHopf algebra of renormalizationButcher groupnumerical integration of ordinary differential equations

Mathematics Subject Classification ID

Noncommutative differential geometry (46L87) Perturbative methods of renormalization applied to problems in quantum field theory (81T15) Feynman diagrams (81T18) Research exposition (monographs, survey articles) pertaining to quantum theory (81-02) Noncommutative geometry (à la Connes) (58B34)

Related Items (11)

Unnamed Item ⋮ Quantum groups and deformation quantization: Explicit approaches and implicit aspects ⋮ A fully nonlinear Feynman-Kac formula with derivatives of arbitrary orders ⋮ Relations between the Hopf algebra and the B-series with new concepts ⋮ Ward identities and combinatorics of rainbow tensor models ⋮ Hopf algebra primitives in perturbation quantum field theory ⋮ B-series methods are exactly the affine equivariant methods ⋮ Is quantum space-time infinite dimensional ⋮ A remainder estimate for branched rough differential equations ⋮ Numerical evaluation of ODE solutions by Monte Carlo enumeration of Butcher series ⋮ Combinatorics of (perturbative) quantum field theory

This page was built for publication: Lessons from quantum field theory: Hopf algebras and spacetime geometries