{"paper":{"title":"Scattering Equations: From Projective Spaces to Tropical Grassmannians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"hep-th","authors_text":"Alfredo Guevara, Freddy Cachazo, Nick Early, Sebastian Mizera","submitted_at":"2019-03-21T10:08:59Z","abstract_excerpt":"We introduce a natural generalization of the scattering equations, which connect the space of Mandelstam invariants to that of points on ${\\mathbb{CP}^1}$, to higher-dimensional projective spaces $\\mathbb{CP}^{k-1}$. The standard, $k=2$ Mandelstam invariants, $s_{ab}$, are generalized to completely symmetric tensors $\\textsf{s}_{a_1a_2\\ldots a_k}$ subject to a `massless' condition $\\textsf{s}_{a_1a_2\\cdots a_{k-2}\\,b\\,b}=0$ and to `momentum conservation'. The scattering equations are obtained by constructing a potential function and computing its critical points. We mainly concentrate on the $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.08904","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}