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Periods and Feynman integrals

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arxiv 0711.4863 v2 pith:GVX36PD7 submitted 2007-11-30 hep-th hep-ph

Christian Bogner , Stefan Weinzierl This is my paper · ORCID
classification hep-thhep-ph
keywords integralslaurentperiodsseriescasecoefficientsconsidercorresponding
verification ladder T0 review T1 audit T2 compute T3 formal

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We consider multi-loop integrals in dimensional regularisation and the corresponding Laurent series. We study the integral in the Euclidean region and where all ratios of invariants and masses have rational values. We prove that in this case all coefficients of the Laurent series are periods.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Emergence of Calabi-Yau manifolds in high-precision black hole scattering

    hep-th 2024-11 unverdicted novelty 8.0 of 10

    At 5PM-1SF order, Calabi-Yau three-fold periods emerge in radiation-reacted observables for classical black hole scattering computed with worldline QFT and advanced IBP/DE methods.

  2. A Graphical Coaction for FRW Integrals from Partial/Relative Twisted (Co)homology

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    Constructs a graphical coaction for all-loop FRW integrals in conformally-coupled scalar theories via twisted (co)homology, with combinatorial description of kinematic flow and a public web app for computation.

  3. Twisted Feynman Integrals: from generating functions to spin-resummed post-Minkowskian dynamics

    hep-th 2025-12 unverdicted novelty 7.0 of 10

    Twisted Feynman integrals are introduced with graded Symanzik polynomials, classified as exponential periods, and shown to have geometry not inferable from generalized Baikov leading singularities.

  4. Fano and Reflexive Polytopes from Feynman Integrals

    hep-th 2025-12 unverdicted novelty 6.0 of 10

    Quasi-finite Feynman integrals produce sparse Fano and reflexive polytopes that encode degenerate Calabi-Yau varieties and link to del Pezzo surfaces, K3 surfaces, and Calabi-Yau threefolds.

  5. Analytic Regression of Feynman Integrals from High-Precision Numerical Sampling

    hep-th 2025-07 conditional novelty 6.0 of 10

    Multi-point lattice reduction on high-precision numerical samples can recover exact analytic expressions for multi-loop Feynman integrals with rational coefficients.

  6. Quantum de Sitter Entropy and Sphere Partition Functions: A-Hypergeometric Approach to Higher Loop Corrections

    hep-th 2024-11 conditional novelty 6.0 of 10

    Scalar and vector Feynman integrals on the sphere are mapped to A-hypergeometric (GKZ) systems via embedding space propagators, enabling algorithmic higher-loop computations.

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