{"paper":{"title":"Amplitude, phase, and complex analyticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"D. Cabrera, J.M. Isidro, P. Fernandez de Cordoba","submitted_at":"2017-02-21T15:34:14Z","abstract_excerpt":"Expressing the Schroedinger Lagrangian ${\\cal L}$ in terms of the quantum wavefunction $\\psi=\\exp(S+{\\rm i}I)$ yields the conserved Noether current ${\\bf J}=\\exp(2S)\\nabla I$. When $\\psi$ is a stationary state, the divergence of ${\\bf J}$ vanishes. One can exchange $S$ with $I$ to obtain a new Lagrangian $\\tilde{\\cal L}$ and a new Noether current $\\tilde{\\bf J}=\\exp(2I)\\nabla S$, conserved under the equations of motion of $\\tilde{\\cal L}$. However this new current $\\tilde{\\bf J}$ is generally not conserved under the equations of motion of the original Lagrangian ${\\cal L}$. We analyse the role"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06440","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":""},"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"}