# On Feynman graphs, matroids, and GKZ-systems

@article{Walther2022OnFG, title={On Feynman graphs, matroids, and GKZ-systems}, author={Uli Walther}, journal={Letters in Mathematical Physics}, year={2022}, volume={112} }

We show in several important cases that the A-hypergeometric system attached to a Feynman diagram in Lee–Pomeransky form, obtained by viewing the coefficients of the integrand as indeterminates, has a normal underlying semigroup. This continues a quest initiated by Klausen and studied by Helmer and Tellander. In the process, we identify several relevant matroids related to the situation and explore their relationships.

## 2 Citations

### Feynman Integral Relations from GKZ Hypergeometric Systems

- MathematicsProceedings of Loops and Legs in Quantum Field Theory — PoS(LL2022)
- 2022

We study Feynman integrals in the framework of Gel’fand-Kapranov-Zelevinsky (GKZ) hypergeometric systems. The latter deﬁnes a class of functions wherein Feynman integrals arise as special cases, for…

### FeynGKZ: a Mathematica package for solving Feynman integrals using GKZ hypergeometric systems

- Mathematics
- 2022

In the Lee-Pomeransky representation, Feynman integrals can be identiﬁed as a sub-set of Euler-Mellin integrals, which are known to satisfy Gel ' fand-Kapranov-Zelevinsky (GKZ) system of partial…

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Abstract
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