Feynman integral relations from parametric annihilators |
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Authors: | Bitoun Thomas Bogner Christian Klausen René Pascal Panzer Erik |
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Institution: | 1.University of Oxford, Oxford, UK ;2.Humboldt-Universit?t zu Berlin, Berlin, Germany ;3.All Souls College (University of Oxford), OX1 4AL, Oxford, UK ; |
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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 integration by parts 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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