MOTIVIC DYSON–SCHWINGER EQUATIONS

DOI10.1142/S0217751X13501029zbMath1277.81086OpenAlexW2165511602MaRDI QIDQ2866863

Ali Shojaei-Fard

Publication date: 9 December 2013

Published in: International Journal of Modern Physics A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0217751x13501029

zbMATH Keywords

Picard-Fuchs equationsDyson-Schwinger equationsConnes-Kreimer Hopf algebraequi-singular connectionsmotivic Feynman rulesuniversal Hopf algebra of renormalization

Mathematics Subject Classification ID

Feynman diagrams (81T18) Nonperturbative methods of renormalization applied to problems in quantum field theory (81T16) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Hopf algebras and their applications (16T05)

Related Items (4)

A new perspective on intermediate algorithms via the Riemann-Hilbert correspondence ⋮ Graph polynomials associated with Dyson-Schwinger equations ⋮ A GEOMETRIC PERSPECTIVE ON COUNTERTERMS RELATED TO DYSON–SCHWINGER EQUATIONS ⋮ Counterterms in the context of the universal Hopf algebra of renormalization

Cites Work

• Anatomy of a gauge theory
• On motives associated to graph polynomials
• The Hopf algebra of Feynman graphs in quantum electrodynamics
• Nonlinear algebra and Bogoliubov's recursion
• Classification of systems of Dyson-Schwinger equations in the Hopf algebra of decorated rooted trees.
• Mixed Hodge structures and renormalization in physics
• Noncommutative geometry, quantum fields and motives
• On the Hopf algebra strucutre of perturbative quantum field theories
• Unique factorization in perturbative QFT
• On overlapping divergences
• New mathematical structures in renormalizable quantum field theories
• Quasi-shuffle products
• Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem
• Renormalization of gauge fields: a Hopf algebra approach
• Faà di Bruno subalgebras of the Hopf algebra of planar trees from combinatorial Dyson-Schwinger equations.
• Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops
• BOGOLUBOV'S RECURSION AND INTEGRABILITY OF EFFECTIVE ACTIONS
• Factorization in Quantum Field Theory: An Exercise in Hopf Algebras and Local Singularities
• FROM DYSON–SCHWINGER EQUATIONS TO THE RIEMANN–HILBERT CORRESPONDENCE
• Periods and Feynman integrals
• Nested sums, expansion of transcendental functions, and multiscale multiloop integrals
• ALGEBRO-GEOMETRIC FEYNMAN RULES
• Renormalization in quantum field theory and the Riemann-Hilbert problem. II: The \(\beta\)-function, diffeomorphisms and the renormalization group.

This page was built for publication: MOTIVIC DYSON–SCHWINGER EQUATIONS