Further investigations into the graph theory of \(\phi^4\)-periods and the \(c_2\) invariant

DOI10.4171/AIHPD/123MaRDI QIDQ2693176

Simone Hu, Oliver Schnetz, Jim Shaw, Karen Yeats

Publication date: 17 March 2023

Published in: Annales de l'Institut Henri Poincaré D. Combinatorics, Physics and their Interactions (AIHPD) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.08751

zbMATH Keywords

Feynman diagramsscalar field theorygraph transformationsFeynman integrals\(c_2\) invariantFeynman periodsgraph identities

Mathematics Subject Classification ID

Graph polynomials (05C31) Feynman diagrams (81T18) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Graph algorithms (graph-theoretic aspects) (05C85)

Related Items (4)

\(c_2\) invariants of hourglass chains via quadratic denominator reduction ⋮ A result on the invariant for powers of primes ⋮ Statistics of Feynman amplitudes in \(\phi^4\)-theory ⋮ Hepp's bound for Feynman graphs and matroids

Uses Software

• Maple
• SageMath
• HyperlogProcedures

Cites Work

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• A few \(c_2\) invariants of circulant graphs
• A \(K3\) in \(\phi^{4}\)
• Single-valued multiple polylogarithms and a proof of the zig-zag conjecture
• Properties of \(c_2\) invariants of Feynman graphs
• Spanning forest polynomials and the transcendental weight of Feynman graphs
• A study on prefixes of \(c_2\) invariants
• On motives associated to graph polynomials
• Quantum periods: a census of \(\phi^4\)-transcendentals
• Quantum field theory techniques in graphical enumeration
• New realizations of modular forms in Calabi-Yau threefolds arising from \(\phi^{4}\) theory
• The Galois coaction on \(\phi^4\) periods
• Geometries in perturbative quantum field theory
• Graphical functions and single-valued multiple polylogarithms
• Graphical functions in parametric space
• \(c_2\) invariants of recursive families of graphs
• Modular forms in quantum field theory
• Hepp's bound for Feynman graphs and matroids
• Some combinatorial interpretations in perturbative quantum field theory
• Knots and Numbers in ϕ⁴ Theory to 7 Loops and Beyond
• A robust generalization of the Legendre transform for QFT
• A special case of completion invariance for the $c_2$ invariant of a graph
• Zeroes of Polynomials Over Finite Fields

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