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.
On the periods of some Feynman integrals
6 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We study the related questions: (i) when Feynman amplitudes in massless $\phi^4$ theory evaluate to multiple zeta values, and (ii) when their underlying motives are mixed Tate. More generally, by considering configurations of singular hypersurfaces which fiber linearly over each other, we deduce sufficient geometric and combinatorial criteria on Feynman graphs for both (i) and (ii) to hold. These criteria hold for some infinite classes of graphs which essentially contain all cases previously known to physicists. Calabi-Yau varieties appear at the point where these criteria fail.
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An extension of the Griffiths-Dwork algorithm produces twisted Picard-Fuchs operators for hypergeometric, elliptic, and Calabi-Yau motives from families of Feynman integrals.
Characterizes numerators yielding finite or evanescent massless pentabox integrals, gives compact generators via momentum basis and Gram determinants, and evaluates lowest-rank cases in polylogarithms and pentagon functions.
Proposes a non-linear geometric framework for multiple zeta values using determinantal integral representations from tropical geometry, moduli spaces, and Feynman integrals, while outlining open questions.
A new open FORM package implements parametric hyperlogarithm integration, demonstrated on zigzag Feynman integrals up to six loops.
citing papers explorer
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Twisted Feynman Integrals: from generating functions to spin-resummed post-Minkowskian dynamics
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.
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Picard-Fuchs Equations of Twisted Differential forms associated to Feynman Integrals
An extension of the Griffiths-Dwork algorithm produces twisted Picard-Fuchs operators for hypergeometric, elliptic, and Calabi-Yau motives from families of Feynman integrals.
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Finite Massless Pentaboxes
Characterizes numerators yielding finite or evanescent massless pentabox integrals, gives compact generators via momentum basis and Gram determinants, and evaluates lowest-rank cases in polylogarithms and pentagon functions.
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Non-linear geometry of multiple zeta values
Proposes a non-linear geometric framework for multiple zeta values using determinantal integral representations from tropical geometry, moduli spaces, and Feynman integrals, while outlining open questions.
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HyperFORM -- a FORM package for parametric integration with hyperlogarithms
A new open FORM package implements parametric hyperlogarithm integration, demonstrated on zigzag Feynman integrals up to six loops.
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