{"paper":{"title":"The Siegel Upper Half Space is a Marsden-Weinstein Quotient: Symplectic Reduction and Gaussian Wave Packets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SG","quant-ph"],"primary_cat":"math-ph","authors_text":"Tomoki Ohsawa","submitted_at":"2015-04-15T16:46:35Z","abstract_excerpt":"We show that the Siegel upper half space $\\Sigma_{d}$ is identified with the Marsden-Weinstein quotient obtained by symplectic reduction of the cotangent bundle $T^{*}\\mathbb{R}^{2d^{2}}$ with $\\mathsf{O}(2d)$-symmetry. The reduced symplectic form on $\\Sigma_{d}$ corresponding to the standard symplectic form on $T^{*}\\mathbb{R}^{2d^{2}}$ turns out to be a constant multiple of the symplectic form on $\\Sigma_{d}$ obtained by Siegel. Our motivation is to understand the geometry behind two different formulations of the Gaussian wave packet dynamics commonly used in semiclassical mechanics. Specifi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03963","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":""},"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"}