{"paper":{"title":"Consequences of the fundamental conjecture for the motion on the Siegel-Jacobi disk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Stefan Berceanu","submitted_at":"2011-10-25T11:29:04Z","abstract_excerpt":"We find the homogenous K\\\"ahler isomorphism $FC$ which expresses the K\\\"ahler two-form on the Siegel-Jacobi domain $\\mathcal{D}^J_1=\\mathbb{C}\\times\\mathcal{D}_1$ as the sum of the K\\\"ahler two-form on $\\mathbb{C}$ and the one on the Siegel ball $\\mathcal{D}_1$. The classical motion and quantum evolution on $\\mathcal{D}^J_1$ determined by a linear Hamiltonian in the generators of the Jacobi group $G^J_1=H_1\\rtimes\\text{SU}(1,1)$ is described by a Riccati equation on $\\mathcal{D}_1$ and a linear first order differential equation in $z\\in\\mathbb{C}$, where $H_1$ denotes the real 3-dimensional He"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5469","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"}