Graphons and renormalization of large Feynman diagrams

DOI10.7494/OpMath.2018.38.3.427zbMath1402.81198OpenAlexW2789653526MaRDI QIDQ4554824

Ali Shojaei-Fard

Publication date: 9 November 2018

Published in: Opuscula Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.7494/opmath.2018.38.3.427

zbMATH Keywords

Dyson-Schwinger equationsgraph functionsConnes-Kreimer renormalization Hopf algebra

Mathematics Subject Classification ID

Trees (05C05) Feynman diagrams (81T18) Nonperturbative methods of renormalization applied to problems in quantum field theory (81T16) Hopf algebras and their applications (16T05) Infinite graphs (05C63)

Related Items

Symmetric Measures, Continuous Networks, and Dynamics, Non-perturbative graph languages, halting problem and complexity, A statistical mechanical model for non-perturbative regimes, Graph polynomials associated with Dyson-Schwinger equations, Kontsevich Graphons, From Dyson-Schwinger equations to quantum entanglement, Non-perturbative β-functions via Feynman graphons, The dynamics of non-perturbative phases via Banach bundles, The complexities of nonperturbative computations, The analytic evolution of Dyson-Schwinger equations via homomorphism densities

Cites Work

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• Convergent sequences of dense graphs. II. Multiway cuts and statistical physics
• Combinatorial Hopf algebras from renormalization
• Anatomy of a gauge theory
• Limits of dense graph sequences
• Convergent sequences of dense graphs. I: Subgraph frequencies, metric properties and testing
• Renormalization automated by Hopf algebra
• Comparison of Hopf algebras on trees.
• QED Hopf algebras on planar binary trees.
• Relating the Connes-Kreimer and Grossman-Larson Hopf algebras built on rooted trees
• A new perspective on intermediate algorithms via the Riemann-Hilbert correspondence
• Quantum field theory. A modern perspective
• Planar diagrams
• Interval graph limits
• Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem
• Moments of two-variable functions and the uniqueness of graph limits
• General Dyson-Schwinger equations and systems
• Renormalization of gauge fields: a Hopf algebra approach
• Faà di Bruno subalgebras of the Hopf algebra of planar trees from combinatorial Dyson-Schwinger equations.
• A Combinatorial Perspective on Quantum Field Theory
• THE GLOBAL β-FUNCTIONS FROM SOLUTIONS OF DYSON–SCHWINGER EQUATIONS
• Graph limits and exchangeable random graphs
• Metrics for sparse graphs
• Combinatorics of rooted trees and Hopf algebras
• Graphons, cut norm and distance, couplings and rearrangements
• Towards the Mathematics of Quantum Field Theory
• A GEOMETRIC PERSPECTIVE ON COUNTERTERMS RELATED TO DYSON–SCHWINGER EQUATIONS
• Counterterms in the context of the universal Hopf algebra of renormalization
• Renormalization of QED with planar binary trees
• Renormalization in quantum field theory and the Riemann-Hilbert problem. II: The \(\beta\)-function, diffeomorphisms and the renormalization group.