{"paper":{"title":"Non--commutative Integration Calculus","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Edwin Langmann","submitted_at":"1995-01-20T13:04:11Z","abstract_excerpt":"We discuss a non--commutative integration calculus arising in the mathematical description of anomalies in fermion--Yang--Mills systems. We consider the differential complex of forms $u_0\\ccr{\\eps}{u_1}\\cdots\\ccr{\\eps}{u_n}$ with $\\eps$ a grading operator on a Hilbert space $\\cH$ and $u_i$ bounded operators on $\\cH$ which naturally contains the compactly supported de Rham forms on $\\R^d$ (i.e.\\ $\\eps$ is the sign of the free Dirac operator on $\\R^d$ and $\\cH$ a $L^2$--space on $\\R^d$). We present an elementary proof that the integral of $d$--forms $\\int_{\\R^d}\\trac{X_0\\dd X_1\\cdots \\dd X_d}$ f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9501092","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"}