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Shift relations among Feynman integrals via s-parametric annihilators

Abstract

Feynman integrals are Mellin integrals: they are the Mellin transform of the graph polynomial of the Feynman diagram taken to the power -d/2, if d denotes the dimension of Minkowski spacetime. It is important to construct relations among Feynman integrals in different dimensions of spacetime. One way to construct such relations is via integration by parts techniques. These IBP relations can be explained via cohomological theories. Also techniques from the theory of D-modules help to construct shift relations, namely by means of Bernstein-Sato operators and s-parametric annihilators, which I explain in this talk. This talk is based on the joint work arXiv:2208.08967 with D. Agostini, C. Fevola, and S. Telen, as well as on ongoing work.

Mirke Olschewski

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Johannes Henn

Max Planck Institute for Physics

Bernd Sturmfels

Max-Planck-Institut für Mathematik in den Naturwissenschaften