{"paper":{"title":"A Convenient Representation Theory of Lorentzian Pseudo-Tensors: $\\mathcal{P}$ and $\\mathcal{T}$ in $\\operatorname{O}(1,3)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.RT"],"primary_cat":"math-ph","authors_text":"Craig McRae","submitted_at":"2025-01-09T17:50:20Z","abstract_excerpt":"A novel approach to the finite dimensional representation theory of the entire Lorentz group $\\operatorname{O}(1,3)$ is presented. It is shown how the entire Lorentz group may be understood as a semi-direct product between its identity component and the Klein four group of spacetime reflections: $\\operatorname{O}(1,3) = \\operatorname{SO}^+(1,3) \\rtimes \\operatorname{K}_4$. This gives way to a convenient classification of tensors transforming under $\\operatorname{O}(1,3)$, namely that there are four representations of $\\operatorname{O}(1,3)$ for each representation of $\\operatorname{SO}^+(1,3)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.05400","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/2501.05400/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"}