{"paper":{"title":"On relationship between canonical momentum and geometric momentum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Q. H. Liu, S. F. Xiao","submitted_at":"2016-05-05T13:55:44Z","abstract_excerpt":"Decompositing of $N+1$-dimensional gradient operator in terms of Gaussian normal coordinates $(\\xi^{0},\\xi^{\\mu})$, ($\\mu=1,2,3,...,N$) and making the canonical momentum $P_{0}$ along the normal direction $\\mathbf{n}$ to be hermitian, we obtain $\\mathbf{n}P_{0}=-i\\hbar\\left( \\mathbf{n}\\partial _{0}-\\mathbf{M}_{0}\\right) $ with $\\mathbf{M}_{0}$ denoting the mean curvature vector on the surface $\\xi^{0}=const.$ The remaining part of the momentum operator lies on the surface, which is identical to the geometric one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01597","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"}