{"paper":{"title":"Time delay for the Dirac equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Ivan Naumkin, Ricardo Weder","submitted_at":"2015-06-26T13:57:13Z","abstract_excerpt":"We consider time delay for the Dirac equation. A new method to calculate the asymptotics of the expectation values of the operator $\\int\\limits_{0} ^{\\infty}e^{iH_{0}t}\\zeta\\left( \\frac{\\left\\vert x\\right\\vert }{R}\\right) e^{-iH_{0}t}dt,$ as $R\\rightarrow\\infty,$ is presented. Here $H_{0}$ is the free Dirac operator and $\\zeta\\left( t\\right) $ is such that $\\zeta\\left( t\\right) =1$ for $0\\leq t\\leq1$ and $\\zeta\\left( t\\right) =0$ for $t>1.$ This approach allows us to obtain the time delay operator $\\delta \\mathcal{T}\\left( f\\right) $ for initial states $f$ in $\\mathcal{H} _{2}^{3/2+\\varepsilon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08079","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1506.08079/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}