{"paper":{"title":"Coherent State Transforms for Spaces of Connections","license":"","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Abhay Ashtekar, Donald Marolf, Jerzy lewandowski, Jos\\'e Mour\\~ao, Thomas Thiemann","submitted_at":"1994-12-05T20:42:32Z","abstract_excerpt":"The Segal-Bargmann transform plays an important role in quantum theories of linear fields. Recently, Hall obtained a non-linear analog of this transform for quantum mechanics on Lie groups. Given a compact, connected Lie group $G$ with its normalized Haar measure $\\mu_H$, the Hall transform is an isometric isomorphism from $L^2(G, \\mu_H)$ to ${\\cal H}(G^{\\Co})\\cap L^2(G^{\\Co}, \\nu)$, where $G^{\\Co}$ the complexification of $G$, ${\\cal H}(G^{\\Co})$ the space of holomorphic functions on $G^{\\Co}$, and $\\nu$ an appropriate heat-kernel measure on $G^{\\Co}$. We extend the Hall transform to the infi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/9412014","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/gr-qc/9412014/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"}