{"paper":{"title":"Feynman integrals as flat bundles over the complement of Landau varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","math.AG","math.MP"],"primary_cat":"math-ph","authors_text":"Stanislav Srednyak","submitted_at":"2017-10-25T16:07:20Z","abstract_excerpt":"We demonstrate that Feynman integrals of a fixed diagram form a flat vector bundle over the complement of Landau varieties that possesses a connection \\begin{equation} \\frac{\\partial}{\\partial p_{i,\\mu}}f_\\beta(p_{i,\\mu})=\\sum_{\\beta'} \\sum_k \\sum_{I_1,...,I_k} \\frac{A^{I_1,...,I_k}_{i,\\mu,\\beta,\\beta'}(p)}{L_{I_1}(p)...L_{I_k}(p)} f_{\\beta'}(p) \\end{equation} where $L_I(p)$ are the Landau polynomials (multidiscriminants). This is the Gauss-Manin connection for the original integral. This result suggests a shift of focus from the integrals to the geometry of the complement of Landau varieties "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09883","kind":"arxiv","version":1},"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"}