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arXiv · 1712.09215

Feynman integral relations from parametric annihilators

Thomas Bitoun·Christian Bogner·Rene Pascal Klausen·Erik Panzer
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Abstract

We study shift relations between Feynman integrals via the Mellin transform through parametric annihilation operators. These contain the momentum space IBP relations, which are well-known in the physics literature. Applying a result of Loeser and Sabbah, we conclude that the number of master integrals is computed by the Euler characteristic of the Lee-Pomeransky polynomial. We illustrate techniques to compute this Euler characteristic in various examples and compare it with numbers of master integrals obtained in previous works.

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Thomas Bitoun, Christian Bogner, Rene Pascal Klausen, Erik Panzer. 2017-12-26. Feynman integral relations from parametric annihilators. https://doi.org/10.1007/s11005-018-1114-8

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