{"paper":{"title":"Ab initio derivation of the quantum Dirac equation by conformal differential geometry: the \"Affine Quantum Mechanics'\"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Enrico Santamato, Francesco De Martini","submitted_at":"2011-07-15T21:40:20Z","abstract_excerpt":"A rigorous \\textit{ab initio} derivation of the (square of) Dirac's equation for a single particle with spin is presented. The general Hamilton-Jacobi equation for the particle expressed in terms of a background Weyl's conformal geometry is found to be linearized, exactly and in closed form, by an \\textit{ansatz} solution that can be straightforwardly interpreted as the \"quantum wave function\" $\\psi_4$ of the 4-spinor Dirac's equation. In particular, all quantum features of the model arise from a subtle interplay between the conformal curvature of the configuration space acting as a potential "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3168","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"}