The number of master integrals as Euler characteristic
October 02, 2018
We give a brief introduction to a parametric approach for the derivation of shift relations between
Feynman integrals and a result on the number of master integrals. The shift relations are obtained
from parametric annihilators of the Lee-Pomeransky polynomial G . By identification of Feynman
integrals as multi-dimensional Mellin transforms, we show that this approach generates every
shift relation. Feynman integrals of a given family form a vector space, whose finite dimension is
naturally interpreted as the number of master integrals. This number is an Euler characteristic of
the polynomial G .
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