Spinor-Helicity Varieties
Yassine El Maazouz, Ana\"elle Pfister, Bernd Sturmfels

TL;DR
This paper explores the geometric and algebraic structures arising from the spinor-helicity formalism in particle physics, focusing on varieties related to Grassmannians, flag varieties, and their tropical and positive geometries.
Contribution
It introduces a detailed study of spinor-helicity varieties, including their combinatorial, algebraic, tropical, and positive geometric aspects, connecting them to scattering amplitudes.
Findings
Identification of subvarieties in Grassmannian products
Analysis of Hadamard products leading to Mandelstam varieties
Connections between these varieties and scattering amplitudes
Abstract
The spinor-helicity formalism in particle physics gives rise to natural subvarieties in the product of two Grassmannians. These include two-step flag varieties for subspaces of complementary dimension. Taking Hadamard products leads to Mandelstam varieties. We study these varieties through the lens of combinatorics and commutative algebra, and we explore their tropicalization, positive geometry, and scattering correspondence.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models
