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Geometric Singularities of Feynman Integrals
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We provide a new method to calculate the full microlocal description of singularities of Feynman integrals. This is done by associating a unique constructible function to the system of partial differential equations (PDEs) annihilating the integral and from this function the singularities can directly be read-off. This function can be constructed explicitly even if the system of PDEs is unknown and describes both the location of the singularities and the number of master integrals on them. Our framework is flexible enough to preform the calculation in any of the Lee-Pomeransky, Feynman, or momentum representations.
Forward citations
Cited by 2 Pith papers
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New algorithm identifies complete Landau singularities of Feynman integrals via Euler characteristic drops over finite fields, applied to non-planar two-loop six-point and massive three-loop graphs.
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Chebyshev polynomial approximations with adaptive sampling solve canonical differential equations for Feynman integrals, demonstrated to be stable and competitive for two-loop five-point cases in double precision.
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