{"paper":{"title":"A self-adjoint decomposition of radial momentum implies that Dirac's introduction of the operator is insightful","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":"2014-11-02T03:51:22Z","abstract_excerpt":"With acceptance of the Dirac's observation that the \\textit{canonical quantization entails using Cartesian coordinates, }we examine the\\textit{\\ }% operator $\\mathbf{e}_{r}P_{r}$ rather than $P_{r}$ itself and demonstrate that there is a decomposition of $\\mathbf{e}_{r}P_{r}$ into two self-adjoint but non-commutative parts, in which one is the total momentum and another is the transverse one. This study renders the operator $P_{r}$ indirectly measurable and physically meaningful."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0203","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"}