Feynman integral relations from parametric annihilators
arXiv:1712.09215 · doi:10.1007/s11005-018-1114-8
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.
v2: new section 3.1 added, several misprints corrected and additional remarks