An introduction to motivic Feynman integrals

DOI10.3842/SIGMA.2021.032zbMath1473.81067arXiv2009.00426OpenAlexW3081883312MaRDI QIDQ2023410

Claudia Rella

Publication date: 3 May 2021

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.00426

zbMATH Keywords

scattering amplitudesGalois theoryFeynman diagramsmultiple zeta valuesHodge structuresTannakian categoriesperiods of motives

Mathematics Subject Classification ID

Galois theory (11R32) Perturbative methods of renormalization applied to problems in quantum field theory (81T15) Feynman diagrams (81T18) Research exposition (monographs, survey articles) pertaining to quantum theory (81-02) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) de Rham cohomology and algebraic geometry (14F40) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) (Equivariant) Chow groups and rings; motives (14C15)

Related Items (2)

\(c_2\) invariants of hourglass chains via quadratic denominator reduction ⋮ Position space equations for banana Feynman diagrams

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Angles, scales and parametric renormalization
• A \(K3\) in \(\phi^{4}\)
• Single-valued multiple polylogarithms and a proof of the zig-zag conjecture
• The multiple zeta value data mine
• The power of perturbation theory
• Algebraic geometry and analytic geometry
• Transcendence of periods: the state of the art
• On motives associated to graph polynomials
• Quantum periods: a census of \(\phi^4\)-transcendentals
• Hodge cycles, motives, and Shimura varieties
• Dihedral quartic approximations and series for \(\pi\)
• Sur l'analysis situs des variétés à \(n\) dimensions
• The Galois coaction on the electron anomalous magnetic moment
• Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case
• Feynman amplitudes, coaction principle, and cosmic Galois group
• Notes on motivic periods
• The Galois coaction on \(\phi^4\) periods
• From positive geometries to a coaction on hypergeometric functions
• Resolution of singularities of an algebraic variety over a field of characteristic zero. II
• The cosmic Galois group and extended Steinmann relations for planar \(\mathcal{N} = 4\) SYM amplitudes
• Closed string amplitudes as single-valued open string amplitudes
• Théorie de Hodge. II. (Hodge theory. II)
• Théorie de Hodge. III
• Categories tannakiennes
• Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops
• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
• Motivic multiple zeta values and superstring amplitudes
• On the decomposition of motivic multiple zeta values
• Periods and Nori Motives
• Groupes fondamentaux motiviques de Tate mixte
• High-Energy Behavior in Quantum Field Theory
• FEYNMAN GRAPH POLYNOMIALS
• Periods and Feynman integrals
• Renormalization and Knot Theory
• Knots and Numbers in ϕ⁴ Theory to 7 Loops and Beyond
• Multiple Zeta Values and Modular Forms in Quantum Field Theory
• Lectures on differential equations for Feynman integrals
• Feynman Categories
• Categories and Sheaves
• The Radiation Theories of Tomonaga, Schwinger, and Feynman
• Space-Time Approach to Quantum Electrodynamics
• Overlapping Divergences and the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math>-Matrix
• Divergent Integrals in Renormalizable Field Theories
• Divergence of Perturbation Theory in Quantum Electrodynamics
• LAURICELLA HYPERGEOMETRIC FUNCTIONS, UNIPOTENT FUNDAMENTAL GROUPS OF THE PUNCTURED RIEMANN SPHERE, AND THEIR MOTIVIC COACTIONS
• Quantum Field Theory
• On the De Rham cohomology of algebraic varieties

This page was built for publication: An introduction to motivic Feynman integrals