{"paper":{"title":"Chen Integrals, Generalized Loops and Loop Calculus","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"J. N. Tavares","submitted_at":"1993-05-29T10:13:47Z","abstract_excerpt":"We use Chen iterated line integrals to construct a topological algebra ${\\cal A}_p$ of separating functions on the {\\it Group of Loops} ${\\bf L}{\\cal M}_p$. ${\\cal A}_p$ has an Hopf algebra structure which allows the construction of a group structure on its spectrum. We call this topological group, the group of generalized loops $\\widetilde {{\\bf L}{\\cal M}_p}$.\n  Then we develope a {\\it Loop Calculus}, based on the {\\it Endpoint} and {\\it Area Derivative Operators}, providing a rigorous mathematical treatment of early heuristic ideas of Gambini, Trias and also Mandelstam, Makeenko and Migdal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9305173","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"}