{"paper":{"title":"Dirac Operators on Configuration Spaces: Fermions with Half-integer Spin, Real Structure, and Yang-Mills Quantum Field Theory","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Jesper M. Grimstrup, Johannes Aastrup","submitted_at":"2024-10-09T14:56:06Z","abstract_excerpt":"In this paper we continue the development of a spectral triple-like construction on a configuration space of gauge connections. We have previously shown that key elements of bosonic and fermionic quantum field theory emerge from such a geometrical framework. In this paper we solve a central problem concerning the inclusion of fermions with half-integer spin into this framework. We map the tangent space of the configuration space into a similar space based on spinors and use this map to construct a Dirac operator on the configuration space. We also construct a real structure acting in a Hilbert"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.07290","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.07290/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}