# Generalised graph Laplacians and canonical Feynman integrals with kinematics

@inproceedings{Brown2022GeneralisedGL, title={Generalised graph Laplacians and canonical Feynman integrals with kinematics}, author={Francis Brown}, year={2022} }

. To any graph with external half-edges and internal masses, we associate canonical integrals which depend non-trivially on particle masses and momenta, and are always ﬁnite. They are generalised Feynman integrals which satisfy graphical relations obtained from contracting edges in graphs, and a coproduct involving both ultra-violet and infra-red subgraphs. Their integrands are deﬁned by evaluating bi-invariant forms which represent stable classes in the cohomology of the general linear group…

## 3 Citations

### Schwinger, ltd: loop-tree duality in the parametric representation

- MathematicsJournal of High Energy Physics
- 2022

We derive a variant of the loop-tree duality for Feynman integrals in the Schwinger parametric representation. This is achieved by decomposing the integration domain into a disjoint union of cells,…

### Graph complexes and Feynman rules

- MathematicsCommunications in Number Theory and Physics
- 2023

We investigate Feynman graphs and their Feynman rules from the viewpoint of graph complexes. We focus on graph homology and on the appearance of cubical complexes when either reducing internal edges…

### In the world of Feynman integrals , a direct connection to moduli spaces of curves was established by the work of

- 2022

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We investigate Feynman graphs and their Feynman rules from the viewpoint of graph complexes. We focus on graph homology and on the appearance of cubical complexes when either reducing internal edges…