Formal solutions of completely integrable Pfaffian systems with normal crossings

Barkatou, Moulay A.; Jaroschek, Maximilian; Maddah, Suzy S.

doi:10.1016/j.jsc.2016.11.018

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Jhep11(2023)2021

B Normal Form By Moser Reduction1

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2023

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“…The existence of a normal form of a logarithmic connection is well-known [23,Proposition 5.4]. Working at the level of Pfaffian matrices, normal form can be found via the standard Moser reduction algorithms of [70,71], which we review in appendix B.…”

Section: Jhep11(2023)202mentioning

confidence: 99%

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Restrictions of Pfaffian systems for Feynman integrals

Chestnov,

Matsubara-Heo,

Munch

et al. 2023

J. High Energ. Phys.

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This work studies limits of Pfaffian systems, a class of first-order PDEs appearing in the Feynman integral calculus. Such limits appear naturally in the context of scattering amplitudes when there is a separation of scale in a given set of kinematic variables. We model these limits, which are often singular, via restrictions of $$ \mathcal{D} $$ D -modules. We thereby develop two different restriction algorithms: one based on gauge transformations, and another relying on the Macaulay matrix. These algorithms output Pfaffian systems containing fewer variables and of smaller rank. We show that it is also possible to retain logarithmic corrections in the limiting variable. The algorithms are showcased in many examples involving Feynman integrals and hypergeometric functions coming from GKZ systems. This work serves as a continuation of [1].

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Section: Jhep11(2023)202mentioning

confidence: 99%

“…ISOLDE [96] and Fuchsia [97]. For the reader's convenience, in this section we review Moser reduction, largely following [70].…”

Section: B Normal Form By Moser Reductionmentioning

confidence: 99%