#feynmanintegrals — Public Fediverse posts

Thursday's #paperOfTheDay: "Almost zero-dimensional quantum field theories" from 1992. That paper considers the behaviour of #quantumMechanics and #quantumFieldTheory close to zero spacetime dimensions. The actual limit D=0, the zero-dimensional field theory, is well understood. The authors now study a (radially symmetric) Schrödinger equation, and then a free field theory, close to D=0. They find that this limit exists (i.e. there is a continuous family of theories for real parameters D which interpolates between the physical and the 0-dimensional theory), and the linear approximation in D already gives numerically meaningful estimates of the physical theory.
This setup is in the same spirit as our #tropicalFieldTheory , but the difference is that the older paper varies D alone, whereas the tropical limit arises when one reduces D and the power of the kinetic term (i.e. spacial decay rate of propagators) simultaneously. Secondly, we now have a much better understanding of analytical properties of #FeynmanIntegrals than 30 years ago, so that we can perform this limit in a mathematical clean way for all graphs of an interacting field theory. https://journals.aps.org/prd/abstract/10.1103/PhysRevD.46.5557

At the EPS-HEP conference last summer, I gave a talk about statistical properties of #FeynmanIntegrals at large loop order. These integrals appear in many places in #physics , I had looked at the special case of scalar theories with quartic self-interaction. The #proceedings of my talk have now been accepted for PoS. The original papers are, as usual, much more detailed and longer, but I believe that the proceedings can be a good way for readers to quickly get a feeling for the type of phenomena one can observe in Feynman integrals at large order in perturbation theory: There are very many integrals, but most of them behave similarly, in a rather structured way with many correlations and only a few outliers. https://doi.org/10.22323/1.485.0462

Over the last 2 years, I did several research projects regarding the statistical properties of #Feynmanintegrals in #QuantumFieldTheory . Basically, we have by now the numerical power to compute millions of these integrals and treat them statistically in a Monte Carlo sense. In summer, I gave a talk about key outcomes at @EPSHEP2025 . The preprint for the proceedings of my talk is now on arxiv. This document is a good starting point to get an overview without reading 150 pages of data tables and plots. https://arxiv.org/abs/2512.06898