In my #dailyPaperChallenge today I have read "Geometry-Kinematics Duality" from 2022. This article is about scalar field theories. From a structural point of view, the non-linear sigma model is the simplest possible scalar field theory, its Lagrangian consists solely of a kinematic term. From this, one can generate all other scalar Lagrangians by introducing a factor that is itself a functional of fields, i.e. it can act by multiplication, but also by derivatives or by "inverse derivatives". It turns out that this object can consistently be interpreted as a metric tensor, analogously to the metric tensor in general relativity, but acting on the "space of field variables" rather than "space of positions". With this, various tree level (i.e. classical, not quantum) #amplitudes can be expressed as geometric objects, for example the Riemann curvature tensor essentially takes the role of the 4-point amplitude. This paper is loosely related to my own work on field redefinition invariance from a few years ago. #paperOfTheDay https://arxiv.org/abs/2202.06972

My article together with Kimia Shaban has appeared in JHEP today. We have examined the #statistics of #Feynmangraph s in #QFT , and how they can be exploited to efficiently compute #amplitudes at high loop order.
The article is open access, and the dataset is freely available from my website if you want to explore statistics and correlations yourself. Predicting the values of these Feynman integrals could also be interesting as a test case for #machinelearning
https://link.springer.com/article/10.1007/JHEP11(2024)038