{"paper":{"title":"A Primer of Group Theory for Loop Quantum Gravity and Spin-foams","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc","math.MP"],"primary_cat":"math-ph","authors_text":"Pierre Martin-Dussaud","submitted_at":"2019-02-22T11:20:51Z","abstract_excerpt":"Calculations in Loop Quantum Gravity (LQG) and spin-foam theory rely heavily on the group theory of SU(2) and SL(2,C). Even though many monographs are devoted to this material, the various tools required (representation theory, harmonic analysis, recoupling theory, ...) are often scattered across different books, each with its own conventions and notations. This was the initial motivation for the present document, which serves three main purposes: a concise introduction for students to the essential mathematical tools of LQG, a convenient compendium of formulae for researchers, and a translati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08439","kind":"arxiv","version":6},"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/1902.08439/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"}