Instead of tracking every single particle, physicists figured out they can just measure the volume of a giant, invisible 'jewel' to explain how the universe works.
March 27, 2026
Original Paper
Landau Analysis in the Grassmannian
arXiv · 2603.25454
The Takeaway
Rather than using messy equations to describe colliding particles, physicists have found that the results match the shape of a geometric object called an "Amplituhedron." This research explores the mathematical rules of this object, suggesting that our reality might be a projection of a higher-dimensional geometric shape.
From the abstract
Momentum twistors for scattering amplitudes in particle physics are lines in three-space. We develop Landau analysis for Feynman integrals in this setting. The resulting discriminants and resultants are identified with Hurwitz and Chow forms of incidence varieties in products of Grassmannians. We study their degrees and factorizations, and the kinematic regimes in which the fibers of the Landau map are rational or real. Identifying this map with the amplituhedron map on positroid varieties, and