{"paper":{"title":"A new perspective on Functional Integration","license":"","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"funct-an","authors_text":"C\\'ecile DeWitt-Morette, Pierre Cartier","submitted_at":"1996-02-08T20:03:42Z","abstract_excerpt":"The core of this article is a general theorem with a large number of specializations. Given a manifold $N$ and a finite number of one-parameter groups of point transformations on $N$ with generators $Y, X_{(1)}, \\cdots, X_{(d)} $, we obtain, via functional integration over spaces of pointed paths on $N$ (paths with one fixed point), a one-parameter group of functional operators acting on tensor or spinor fields on $N$. The generator of this group is a quadratic form in the Lie derivatives $\\La_{X_{(\\a)}}$ in the $X_{(\\a)}$-direction plus a term linear in $\\La_Y$.\n  The basic functional integra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"funct-an/9602005","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"}