{"paper":{"title":"An Exact Formulation of the Time-Ordered Exponential using Path-Sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP"],"primary_cat":"math-ph","authors_text":"D. Jaksch, K. Lui, P.-L. Giscard, S. J. Thwaite","submitted_at":"2014-10-24T10:09:57Z","abstract_excerpt":"We present the path-sum formulation for $\\mathsf{OE}[\\mathsf{H}](t',t)=\\mathcal{T}\\,\\text{exp}\\big(\\int_{t}^{t'}\\!\\mathsf{H}(\\tau)\\,d\\tau\\big)$, the time-ordered exponential of a time-dependent matrix $\\mathsf{H}(t)$. The path-sum formulation gives $\\mathsf{OE}[\\mathsf{H}]$ as a branched continued fraction of finite depth and breadth. The terms of the path-sum have an elementary interpretation as self-avoiding walks and self-avoiding polygons on a graph. Our result is based on a representation of the time-ordered exponential as the inverse of an operator, the mapping of this inverse to sums of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6637","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"}