{"paper":{"title":"A unified-description of curvature, torsion, and non-metricity of the metric-affine geometry with the M\\\"{o}bius representation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Kyosuke Tomonari","submitted_at":"2023-12-17T10:36:20Z","abstract_excerpt":"We establish the mathematical fundamentals for a unified description of curvature, torsion, and non-metricity 2-forms in the way extending the so-called M\\\"{o}bius representation of the affine group, which is the method to convert the semi-direct product into the ordinary matrix product, to revive the fertility of gauge theories of gravity. First of all, we illustrate the basic concepts for constructing the metric-affine geometry. Then the curvature and torsion 2-forms are described in a unified manner by using the Cartan connection of the M\\\"{o}bius representation of the affine group. In this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.11558","kind":"arxiv","version":3},"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/2312.11558/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"}