Renormalization automated by Hopf algebra

DOI10.1006/jsco.1999.0283zbMath1049.81048arXivhep-th/9810087OpenAlexW2024131740MaRDI QIDQ1300631

Dirk Kreimer, David J. Broadhurst

Publication date: 1999

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9810087

zbMATH Keywords

Reduce code

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Model quantum field theories (81T10) Perturbative methods of renormalization applied to problems in quantum field theory (81T15) Feynman diagrams (81T18) Software, source code, etc. for problems pertaining to quantum theory (81-04)

Related Items

Unnamed Item, Graphons and renormalization of large Feynman diagrams, The Hopf algebra of Feynman graphs in quantum electrodynamics, A measure theoretic perspective on the space of Feynman diagrams, Updown categories: generating functions and universal covers, From Dyson-Schwinger equations to quantum entanglement, The dynamics of non-perturbative phases via Banach bundles, The complexities of nonperturbative computations, Combinatoric explosion of renormalization tamed by Hopf algebra: 30-loop Padé-Borel resummation., Exact solutions of Dyson-Schwinger equations for iterated one-loop integrals and propagator-coupling duality, Hopf algebra primitives in perturbation quantum field theory, Combinatorics of rooted trees and Hopf algebras, Unique factorization in perturbative QFT, Renormalization and Mellin Transforms, A free subalgebra of the algebra of matroids, Combinatorics of (perturbative) quantum field theory, Finite dimensional comodules over the Hopf algebra of rooted trees, New mathematical structures in renormalizable quantum field theories

Cites Work

• Unnamed Item
• Unnamed Item
• Proof of the Bogoliubov-Parasiuk theorem on renormalization
• Über die Multiplikation der Kausalfunktionen in der Quantentheorie der Felder
• Factoring polynomials with rational coefficients
• Hopf algebras, renormalization and noncommutative geometry
• On the Hopf algebra strucutre of perturbative quantum field theories
• Hopf algebras, cyclic cohomology and the transverse index theorem
• Feynman diagrams as a weight system: four-loop test of a four-term relation.
• Convergence of Bogoliubov's method of renormalization in momentum space
• Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops
• Polynomial Factorization and Nonrandomness of Bits of Algebraic and Some Transcendental Numbers
• Iterated path integrals
• Renormalization and Knot Theory
• Weight Systems from Feynman Diagrams
• Knots and Numbers in ϕ⁴ Theory to 7 Loops and Beyond
• Knots and Feynman Diagrams
• Chen's iterated integral represents the operator product expansion