Magic relations in Feynman integral families coincide with higher-dimensional critical varieties, enabling a practical test to detect and handle them.
Mizera,Status of Intersection Theory and Feynman Integrals,PoSMA2019(2019) 016 [2002.10476]
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A parity-split IBP system for n-propagator families in de Sitter space is identified, along with a conjecture that dlog-form differential equations extend to dS integrands with Hankel functions, verified for the one-loop bubble.
Branch representation reduces the variable count for intersection-theory-based Feynman integral reduction to at most 3L-3 for L-loop integrals regardless of leg number.
An extension of the Griffiths-Dwork algorithm produces twisted Picard-Fuchs operators for hypergeometric, elliptic, and Calabi-Yau motives from families of Feynman integrals.
Contour equivalence in Feynman parameterization yields universal reduction formulas for one-loop integrals without integration-by-parts.
Reversing the direction of tubing evolution yields splitting rules that reproduce the kinematic flow differential equations at tree level and suggest time emerges from kinematic space in conformally coupled scalar models and tr phi^3 theory.
citing papers explorer
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Magic Relations and Critical Varieties of Feynman Integrals
Magic relations in Feynman integral families coincide with higher-dimensional critical varieties, enabling a practical test to detect and handle them.
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Loop integrals in de Sitter spacetime: The parity-split IBP system and $\mathrm{d}\log$-form differential equations
A parity-split IBP system for n-propagator families in de Sitter space is identified, along with a conjecture that dlog-form differential equations extend to dS integrands with Hankel functions, verified for the one-loop bubble.
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Feynman integral reduction with intersection theory made simple
Branch representation reduces the variable count for intersection-theory-based Feynman integral reduction to at most 3L-3 for L-loop integrals regardless of leg number.
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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.
-
Feynman Integral Reduction without Integration-By-Parts
Contour equivalence in Feynman parameterization yields universal reduction formulas for one-loop integrals without integration-by-parts.
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An Alternative Viewpoint on Kinematic Flow from Tubing Splitting
Reversing the direction of tubing evolution yields splitting rules that reproduce the kinematic flow differential equations at tree level and suggest time emerges from kinematic space in conformally coupled scalar models and tr phi^3 theory.