Computability in QFT and tropical QFT
In general, observables in QFTs can only be computed perturbatively using Feynman integrals. In this talk, which is based on arXiv:2008.12310 and arXiv:2204.06414, I will address some questions on the computability of such observables. By looking at QFT through the lens of tropical geometry, one can see that the runtime of such computations is dominated by the time it takes to understand the structure of certain polytopes. In the case of scalar QFTs on Euclidean space the relevant polytopes turn out to be generalized permutahedra, whose structure is well-understood thanks to the works of Postnikov, Aguiar and Ardila. Using these insights, results in a new algorithm for Feynman integral evaluation that exceeds the capabilities of existing methods by multiple orders of magnitude, while being easy to implement. I will also briefly discuss current wip that extends these findings to QFTs on Minkowski spacetime.