{"paper":{"title":"Time-Dependent Hilbert Spaces, Geometric Phases, and General Covariance in Quantum Mechanics","license":"","headline":"","cross_cats":["gr-qc","hep-th","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Ali Mostafazadeh","submitted_at":"2003-06-30T09:49:32Z","abstract_excerpt":"We investigate consequences of allowing the Hilbert space of a quantum system to have a time-dependent metric. For a given possibly nonstationary quantum system, we show that the requirement of having a unitary Schreodinger time-evolution identifies the metric with a positive-definite (Ermakov-Lewis) dynamical invariant of the system. Therefore the geometric phases are determined by the metric. We construct a unitary map relating a given time-independent Hilbert space to the time-dependent Hilbert space defined by a positive-definite dynamical invariant. This map defines a transformation that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0306200","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"}