{"paper":{"title":"First-order differential equations for a particle with spin $S = 1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"B. E. Grinyuk","submitted_at":"2018-01-25T14:34:00Z","abstract_excerpt":"A system of first-order differential equations for a particle with nonzero mass and spin $S = 1$ is constructed. As distinct from the Proca-Duffin-Kemmer (PDK) equations, the system has the form of the dynamical equation $i\\hbar\\partial_t\\hat{\\Psi}=\\hat{\\mathrm{H}}\\hat{\\Psi}$ (with constraints) with a Hamiltonian linear in momentum. The six-component wave function yields the positive-definite probability density $\\hat{\\Psi}^{\\dagger}\\hat{\\Psi}\\geq 0$. The system of equations has much in common with the Dirac and Maxwell equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08414","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"}