Motives associated to graphs

DOI10.1007/s11537-007-0648-9zbMath1161.11021OpenAlexW2058269050MaRDI QIDQ1000338

Spencer Bloch

Publication date: 6 February 2009

Published in: Japanese Journal of Mathematics. 3rd Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11537-007-0648-9

zbMATH Keywords

graphrenormalizationHopf algebraperiodFeynman diagramgraph polynomialmotiveSchwinger integral

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Perturbative methods of renormalization applied to problems in quantum field theory (81T15) Feynman diagrams (81T18) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) (14F43) Polylogarithms and relations with (K)-theory (11G55)

Related Items

A new perspective on intermediate algorithms via the Riemann-Hilbert correspondence ⋮ Feynman diagrams and their algebraic lattices ⋮ SOME RESULTS ON AN ALGEBRO-GEOMETRIC CONDITION ON GRAPHS ⋮ The Ponzano-Regge model and parametric representation ⋮ ALGEBRO-GEOMETRIC FEYNMAN RULES ⋮ Renormalization and Periods in Perturbative Algebraic Quantum Field Theory ⋮ FEYNMAN GRAPH POLYNOMIALS ⋮ On the establishment of the Takagi lectures ⋮ Regularized integrals on Riemann surfaces and modular forms

Cites Work

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• Variation of mixed Hodge structure. I
• Modules de Hodge polarisables. (Polarisable Hodge modules)
• On motives associated to graph polynomials
• Quantum field theory techniques in graphical enumeration
• Counting points on varieties over finite fields related to a conjecture of Kontsevich
• Cohomology of local systems on the complement of hyperplanes
• Matroids, motives, and a conjecture of Kontsevich.
• On a theorem of Kontsevich
• Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem
• Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops
• Quantum fields and motives
• Multiple $\zeta$-motives and moduli spaces $\overline{\mathcal{M}}_{0,n}$
• Knots and Numbers in ϕ⁴ Theory to 7 Loops and Beyond
• Mixed Hodge modules
• Renormalization in quantum field theory and the Riemann-Hilbert problem. II: The \(\beta\)-function, diffeomorphisms and the renormalization group.