{"paper":{"title":"Dirac Equation with External Potential and Initial Data on Cauchy Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"D.-A. Deckert, F. Merkl","submitted_at":"2014-04-04T21:40:09Z","abstract_excerpt":"With this paper we provide a mathematical review on the initial-value problem of the one-particle Dirac equation on space-like Cauchy hypersurfaces for compactly supported external potentials. We, first, discuss the physically relevant spaces of solutions and initial values in position and mass shell representation; second, review the action of the Poincar\\'e group as well as gauge transformations on those spaces; third, introduce generalized Fourier transforms between those spaces and prove convenient Paley-Wiener- and Sobolev-type estimates. These generalized Fourier transforms immediately a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1401","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"}